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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

In Exercises 1–30, find the domain of each function. f(x) = 2(x + 5)
In Exercises 1–16, use the graph of y = f(x) to graph each function g. y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–10, find f(g(x)) and g( f(x)) and determine whether each pair of functions f and g are inverses of each other. f(x) = 6x and g(x) X 6
In Exercises 1–30, find the domain of each function. f(x) = 3(x-4)
Fill in each blank so that the resulting statement is true.The midpoint of a line segment whose endpoints are (x1, y1) and (x2, y2) is (______ ,_________ ).
Fill in each blank so that the resulting statement is true.The slope, m, of a line through the distinct points (x1, y1) and (x2, y2) is given by the formula m =_______ .
In Exercises 1–10, find f(g(x)) and g( f(x)) and determine whether each pair of functions f and g are inverses of each other. f(x) = 4x and g(x) = X
Fill in each blank so that the resulting statement is true.We exclude from a function’s domain real numbers that result in a square root of a/an__________ number.
Fill in each blank so that the resulting statement is true.A set of ordered pairs in which each member of the set of first components corresponds to exactly one member of the set of second components
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(5, 1) and (8, 5)
Fill in each blank so that the resulting statement is true.If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative______ of f. If f(b) < f(x) in an
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(2, 3) and (14, 8)
Fill in each blank so that the resulting statement is true.If the function g is the inverse of the function f, then f(g(x)) =______ and g( f(x)) =________ .
Fill in each blank so that the resulting statement is true.We exclude from a function’s domain real numbers that cause division by_________ .
Fill in each blank so that the resulting statement is true.The distance, d, between the points (x1, y1) and (x2, y2) in the rectangular coordinate system is d =_______ .
Fill in each blank so that the resulting statement is true.The notation f -1 means the________ of the function f.
In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is
Fill in each blank so that the resulting statement is true.(f + g)(x) =_________ .
Fill in each blank so that the resulting statement is true.The notation f(x) describes the value of________ at________ .
Fill in each blank so that the resulting statement is true.The graph of y = -f(x) is the graph of y = f(x) reflected about the_______ .
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(4, -1) and (-6, 3)
In Exercises 1–30, find the domain of each function. g(x) 3 x - 4
Fill in each blank so that the resulting statement is true.The graph of an equation is symmetric with respect to the______ if substituting -x for x in the equation results in an equivalent equation.
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x + 1) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–12, use the graph to determinea. intervals on which the function is increasing, if any.b. intervals on which the function is decreasing, if any.c. intervals on which the function is
Fill in each blank so that the resulting statement is true.A function f has an inverse that is a function if there is no________ line that intersects the graph of f at more than one point. Such a
Let a function f be the line graph connecting the data points (1, 2), (4,9), and (6,3). (a) Write the formula for a piecewise-linear function f that passes through these data points whose domain
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. 3=5x 3
Solve the equation (a) Graphically, (b) Numerically, and (c) Symbolically. Then solve the related inequality. |4x7| = 5, |4x - 7| ≥ 5
The table shows equivalent temperatures in degrees Celsius and degrees Fahrenheit.(a) Plot the data with Fahrenheit temperature on the x-axis and Celsius temperature on the y-axis. What type of
The graph depicts the distance y that a person driving a car on a straight road is from home after x hours. Interpret the graph. What speeds did the car travel? Distance (miles) 2 Time (hours)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. 4x - 3y = 6
Use the intersection-of-graphs method to solve the equation. Then solve symbolically. -(x + 1)2 = 2x
Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. 1.238x +0.998 1.23 (3.987-2.1x)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. 0.2x + 0.4y= 0.8
Solve the equation symbolically. Then solve the related inequality. |2.1x0.7| = 2.4, 2.1x -0.7 2.4
Let y vary directly with x. Complete the following. Find y when x = 1, if y = when x = 3.
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. y = x= 1
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. -4 < 55-3.1x 4 < 17
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. 2x-4 = 0
Determine the x- and y-intercepts on the graph of the equation. Graph the equation. y = 8x-5
Solve the equation symbolically. Then solve the related inequality. 1 - X
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. 1.59.10.5x6.8
Find the constant of proportionality k and the undetermined value in the table if y is directly proportional to x. x y 3 7.5 5 12.5 6 15 8 ?
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. -1-²x = = 0
Solve the equation symbolically. Then solve the related inequality. |3x| + 5 = 6, |3x| +5>6
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. 2x = -(3x)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. y=-1.5x + 15
The table lists the actual annual cost y to drive a midsize car 15,000 miles per year for selected years X.(a) Predict whether the correlation coefficient is positive, negative, or zero. (b) Find a
Find the constant of proportionality k and the undetermined value in the table if y is directly proportional to x. x 1.2 4.3 5.7 3.96 14.19 18.81 ? 23.43
Let y vary directly with x. Complete the following.Find y when x = 1.3, if y = 7.2 when x = 5.2.
A driver of a car is initially 455 miles from home, traveling toward home on a straight freeway at 70 miles per hour. (a) Write a formula for a linear function f that models the distance between
Solve the equation symbolically. Then solve the related inequality. |5x – 0.3| = −4, |5x – 0.3| > →4 -
Solve the equation symbolically. Then solve the related inequality. - 두 - x] S | - H =
Initially, a tank contains 20 gallons of a 30% anti-freeze solution. How many gallons of an 80% antifreeze solution should be added to the tank in order to increase the concentration of the
Solve the equation symbolically. Then solve the related inequality. |x|- 10 = 25, |x-10 < 25
Solve the inequality. Write the solution in interval notation. |3x - 1| < 8
In 2012 the population of a city was 143,247, and in 2016 it was 167,933. Estimate the population in 2014.
Solve the inequality. Write the solution in interval notation. E > 1
Solve the inequality. Write the solution in interval notation. |7 - 4x = 11
Solve the inequality. Write the solution in interval notation. |-}x| < 1
Solve the inequality. Write the solution in interval notation. 6 IV
Solve the inequality. Write the solution in interval notation. |15 = x < 7
Solve the inequality. Write the solution in interval notation. |-3x + 1 ≤ 5
Suppose that one worker can shovel snow from a storefront sidewalk in 50 minutes and another worker can shovel it in 30 minutes. How long will it take if they work together?
Due to acid rain, the percentage of lakes in Scandinavia that lost their population of brown trout increased dramatically between 1940 and 1975. Based on a sample of 2850 lakes, this percentage can
Suppose the tank is modified so that it has a second inlet pipe, which flows at a rate of 2 gallons per minute. Interpret the graph by determining when each inlet and outlet pipe is open or closed.
An athlete traveled 13.5 miles in 1 hour and 48 minutes, jogging at 7 miles per hour and then at 8 miles per hour. How long did the runner jog at each speed?
Solve the inequality. Write the solution in interval notation. |3x - 5|
The table at the top of the next column lists the cost in millions of dollars for a 30-second Super Bowl commercial for selected years.(a) Find a linear function f that models the data. (b) Estimate
Solve the inequality. Write the solution in interval notation. |-5-2x| > 1
Solve the inequality. Write the solution in interval notation. |9x + 1| < 10
At one time the Thames River in England supported an abundant community of fish. Pollution then destroyed all the fish in a 40-mile stretch near its mouth for a 45-year period beginning in 1915.
For altitudes up to 4 kilometers, moist air will cool at a rate of about 6°C per kilometer. If the ground temperature is 25°C, at what altitudes would the air temperature be from 5°C to 15°C?
The actual length of a side of a building is 52.3 feet. How accurately must an apprentice carpenter measure this side to have the relative error in the measurement be less than 0.003 (0.3%)?
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures
If a quantity is measured to be Q and its exact value is A, then the relative error in Q isIf the exact value is A = 35 and you want the relative error in Q to be less than or equal to 0.02 (or 2%),
An aluminum can should have a diameter D of 3 inches with a maximum error tolerance that is less than 0.004 inch. (a) Write an absolute value statement that describes this situation. (b)
The classic iPod is 10.5 millimeters thick. Suppose that the actual thickness T of any particular iPod has a maximum error tolerance that is less than 0.05 millimeter.(a) Write an absolute value
A part for a machine must fit into a hole and must have a diameter D that is less than or equal to 2.125 inches. The diameter D cannot be less than this maximum diameter of 2.125 inches by more than
Find the point-slope form of the line pass- ing through the given points. Use the first point as (x1, y1). (-3,4), (2,5)
Suppose that a 12-inch ruler must have the correct length L to within 0.0002 inch. (a) Write an absolute value inequality for L that describes this requirement. (b) Solve this inequality
The exact perimeter P of a square is 50 feet. What measured lengths are possible for the side S of the square to have relative error in the perimeter that is less than or equal to 0.04 (or 4%)?
Find the point-slope form of the line passing through the given points. Use the first point as (x1, y1). (1,-6), (-7,5)
Find the point-slope form of the line passing through the given points. Use the first point as (x1, y1). Then convert the equation to slope-intercept form and write a formula for a function f whose
Let a ≠ 0.Solve |x| = 3.
EvaluateRound your answer to the nearest hundredth. 4+ √₂ 4-√₂
(a) Solve the equation |2x - 1| = 5.(b) Use part (a) to solve the absolute value inequalities |2x - 1| ≤ 5 and |2x - 1| > 5. Use interval notation.
Explain how to solve |ax + b| = k with k > 0 symbolically. Give an example.
Rewrite √4x2 by using an absolute value.
Explain how to use the solutions to ax + b = k with k > 0 to solve the inequalities and |ax + b| > k. Give an example. ax + b < k
Write 123,000 and 0.0051 in scientific notation.
Let a ≠ 0.Solve |x| ≤ 3.
Let δ be a positive number and let x and e be real numbers. Write an absolute value inequality that expresses that the distance between x and c on the number line is less than δ.
Let ϵ be a positive number, L be a real number, and be a function. Write an absolute value inequality that expresses that the distance between f(x) and L on the number line is less than ϵ.
Graph y = |3x - 2| by hand.
Write 6.7 x 106 and 1.45 x 10-4 in standard form.

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