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mathematics
college algebra graphs and models
Questions and Answers of
College Algebra Graphs And Models
Let a ≠ 0.Solve |x| > 3.
Let a ≠ 0.Solve |ax + b| ≤ -2.
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 dew point decreases as altitude increases. If the dew point on the ground is 80°F, then the dew point x miles high is D = 80 - (29/5)x.(a) Determine the altitudes x where the dew point D is
The air temperature decreases as altitude increases. If the ground temperature is 80°F, then the air temperature x miles high is T = 80 - 19x. (a) Determine the altitudes x where the air
A human cannonball plans to travel 180 feet and land squarely on a net with a 70-foot-long safe zone. (a) What distances D can this performer travel and still land safely on the net? (b)
The maximum and minimum lawful speeds S on an interstate highway satisfy the equation |S 57.5| = 17.5. Find the maximum and minimum speed limits.
The salary S for a mechanic must be within $8000 of $60,000. Write an absolute value inequality that describes possible salaries for the mechanic. Give the salary range of S.
If the domain of y = f(x) is [-2, 3] and the range is (-5, 8], find the domain and range of each of the following. (a) y = -f(x)| +2 (b) y = -f(x) - 3 (c) y = f(x - 1)| + 1
If a and b are fixed real numbers with a ≠ 0, then give the domain and range of each function. (a) f(x) = ax + bl (b) g(x) = ax + b + 1 (c) h(x) = ax + b|-1
Graph by hand. (a) Find the x-intercept. (b) Determine where the graph is increasing and where it is decreasing. |I + x| = Á
A graph of y = f(x) is given. Find the domain and range of y = f(x) and of y = |f(x)|. Use interval notation. 3
A graph of y = f(x) is given. Find the domain and range of y = f(x) and of y = |f(x)|. Use interval notation. -2- y = f(x) 3
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
The temperature T'in a freezer is always within 5°F of -10°F. Write an absolute value inequality that describes possible temperatures in the freezer. Give the temperature range of T.
If the range of f(x) is given by (-4, 5), what is the range of |f(x)|?
Find the midpoint of the line segment with endpoints (5,-2) and (-3,1).
Find the average rate of change of f(x) =-3x + 8 from -2 to 3.
Let a ≠ 0.Rewrite √(ax + b)2 by using an absolute value.
Find the exact distance between (-3, 5) and (2, -3).
Let a ≠ 0.Rewrite √36a2 by using an absolute value.
Let a ≠ 0.Solve |ax + b| = 0.
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
Find the standard equation of a circle with center (-2, 3) and radius 7.
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
Evaluate -52 - 2 - (10 - 2)/(5 - 1) by hand.
Solve |x + 1| = |2x|.
Let a ≠ 0.Describe the graph of y = |ax + b|.
Solve the linear equation either symbolically or graphically. TX + 1 = 6
Solve the linear equation either symbolically or graphically. x-4 2 + 1 - 2x 3
Solve the absolute value equation. |-10x| = -100
Solve the absolute value equation. |-5x| = –2 -2
Use a table to solve each linear equation numerically to the nearest tenth. √7-3x - 2.1(1 + x) = 0
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = 2x
Use a table to solve each linear equation numerically to the nearest tenth. 3.1x0.22(x - 1.7) = 0
Solve the absolute value equation. ||2x - 7기 = 15
Find the domain and range of the function shown in the graph. Evaluate f(-1). (a) -3-2 32 1 2 (b) 32 2/3
Graph by hand. (a) Find the x-intercept. (b) Determine where the graph is increasing and where it is decreasing. y = [1 - x|
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = x
Solve the absolute value equation. |4x + 3 = 27
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = 2x - 4
Graph by hand. (a) Find the x-intercept. (b) Determine where the graph is increasing and where it is decreasing. y = |2x - 3|
Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. 4(6-x) -4x + 24
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = 3x - 3 -
Solve x + 1 = 2x - 2 graphically and numerically.
Graph by hand. (a) Find the x-intercept. (b) Determine where the graph is increasing and where it is decreasing. |1 + x²| = 4
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = 6 - 2x
Do the following. (a) Graph y = f(x). (b) Use the graph of y = f(x) to sketch a graph of the equation y = |f(x)|. (c) Determine the x-intercept for the graph of y = |(x)|. y = 2 - 4x
Find the slope-intercept form of the equation of a line satisfying the conditions. Perpendicular to y = x, passing through (3,0)
Graph f by hand. (a) f(x) = 3 - 2x (b) f(x) = |x + 1|
Find the slope-intercept form of the equation of a line satisfying the conditions.Slope 7, passing through (-3,9)
Determine if the graph represents a function. Explain your answer. -2 3
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write a formula for f. (c) Find any zeros of f. -3-2- y = f(x) 3
Find the slope-intercept form of the equation of a line satisfying the conditions.Passing through (2, -4) and (7,-3)
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write a formula for f. (c) Find any zeros of f. 2 y = f(x)
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) >
Find the slope-intercept form of the equation of a line satisfying the conditions.Passing through (1, -1), parallel to y = 3x + 1
Find the slope-intercept form of the equation of a line satisfying the conditions.Passing through the point (-2, 1), perpendicular to the line y = 2(x + 5) - 22
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) >
Find the slope-intercept form of the equation of a line satisfying the conditions.Parallel to the line segment connecting (0, 3) and (6, 0), passing through (1, -7)
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible. Passing through (1,-5) and (-3,-)
Determine the x- and y-intercepts for the graph of the equation. Graph the equation. 5x - 4y = 20
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) >
Find the average rate of change of the function f(x) = x2 - 2x + 1 from x = 1 to x = 2.
Write a formula for a function f that computes the cost of taking x credits if credits cost $80 each and fees are fixed at $89.
Find an equation of the specified line.Parallel to the y-axis, passing through (6, -7)
Find the difference quotient for f(x) = 2x2 - x.
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible. Passing through the point (-3, 2) and perpendicular to the line y = x - 7
Determine the x- and y-intercepts for the graph of the equation. Graph the equation. le I
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) >
Find an equation of the specified line.Parallel to the x-axis, passing through (-3,4)
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) > 0,
Find an equation of the specified line.Horizontal, passing through (1, 3)
Find an equation of the specified line.Vertical, passing through (1.5, 1.9)
Solve the linear equation either symbolically or graphically. 5x-(4-3x) = (2x + 3) -
Find an equation of the specified line.Vertical with x-intercept (2.7, 0)
Solve the linear equation either symbolically or graphically. 5x – 25 = 10 -
The graph of y = f(x) is shown. Complete the following and use interval notation when appropriate. (a) Identify any x-intercepts or y-intercepts. (b) Determine the x-values that satisfy f(x) >
Solve the linear equation either symbolically or graphically. -2(3x-7) + x = 2x-1
Find an equation of the specified line.Horizontal with y-intercept (0, -8)
Determine the x- and y-intercepts on the graph of the equation. Graph the equation. -2x + 3y = 6
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. x = 2y - 3
Solve the absolute value equation. |-2x| = 4
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible.Slope 30, passing through (2002, 50)
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible.Passing through ment connecting (-3, 5) and parallel to the line seg- (2.4, 5.6) and (3.9,8.6)
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible.Parallel to the y-axis and passing through (-1, 3)
Solve the absolute value equation. |3x| = 6
Solve the linear equation either symbolically or graphically. 5(4-2x) = 30
Write an equation of a line satisfying the given conditions. Use slope-intercept form whenever possible.Perpendicular to the y-axis and passing through the origin
Solve the absolute value equation. |-9- 4x = 1
SolveIs this equation either an identity or a contradiction? 2x (5-x) = ¹ = 4x + 5(x - 2).
Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. (4x - 3) + 2 = 3x = (1 + x)
Solve the absolute value equation. |-7 = 3x| = 22
Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. 52(4-3x) + x = 4(x − 3)
Solve the absolute value equation. ||5x - 7기 = 2
Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. x-3 4 3 +21-50 - 5(2-7x) = 36x 43 4
Express each inequality in interval notation. x < 5
Solve the absolute value equation. |-3x - 2 = 5
Express each inequality in interval notation. x < -2 or x > 2
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