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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = (x + h)² - k
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = √x + h-k
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = (xh)² + k
Use the vertex formula to determine the vertex on the graph of f. f(x) = x² + 8x - 5
Use the vertex formula to determine the vertex on the graph of f. f(x) = -3x² + 2x - 4
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = √x-h+k
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. f(x) = x²; right 2 units, downward 3 units
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. f(x)=x²-x-2; right 2 units, upward 3 units
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. f(x) = 3x - 4; left 3 units, upward 1 unit
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. f(x) = x² - 4x + 1; left 6 units, upward 4 units
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = 3x² + 2x - 5 (a) Shifted left 3 units (b) Shifted downward 4
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = 2x²-3x + 2 (a) Shifted right 8 units (b) Shifted upward 2 units
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. f(x) = x² + 2x - 1; left 3 units, downward 2 units
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = 2x² (a) Shifted right 2 units and upward 4 units (b) Shifted
Find an equation that shifts the graph of f by the desired amounts. Do not simplify. Graph f and the shifted graph in the same xy-plane. ƒ(x) = 5 − 3x − £x²; right 5 units, downward 8 units -
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = √x (a) Shifted right 4 units, reflected about the x-axis (b)
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = 5x² (a) Shifted left 10 units and downward 6 units (b) Shifted
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = 3x² 3x + 2 (a) Shifted right 2000 units and upward 70
Use the imaginary unit i to simplify each expression. (a) V-16 (c) √-5. V-15 (b) V-48
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = |x| (a) Shifted right 4 units and downward 3 units (b) Shifted
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x) + 2 (b) y = f(x - 2) - 1 (c) y = -f(x) (-2,2) y (2.2) 2 y=f(x) (0, -2)
Write a formula for a function g whose graph is similar to f(x) but satisfies the given conditions. Do not simplify the formula. f(x) = √x (a) Reflected about the x-axis, shifted left 2 units (b)
Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. x² + y² = 4; right 3 units, downward 4 units
Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. x² + y² = 9; right 2 units, downward 6 units
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x + 3) - 2 (b) y = f(-x) (c) y = f(x) - y = f(x) 3
Find the average rate of change of f(x) = -6x2 + 7x + 5 from 2 to 4.
Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. x² + y² = 5; left 5 units, upward 3 units
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x + 1) (b) y = -f(x) (c) y = 2 f(x) (-2.0) (0,2) (2.0) y = f(x) ➤X
Find the difference quotient for f(x) = x2 - 2x.
Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. ² + y² = 7; left 3 units, downward 7 units
Use the graph and the given f(x) t complete the following. (a) Find any x-intercepts. (b) Find the complex zeros of f. √√(x) = -2x² - 4x + 5 2 234
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x + 1) + 1 (b) y = -f(x) - 1 (c) y = f(2x) (-1.2) (-2,0) y = f(x) (0, 0) (2.0) (1.-2)
Use the graph and the given f(x) t complete the following. (a) Find any x-intercepts. (b) Find the complex zeros of f. 2 1f(x)= -1+2x-2x² 7
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x) - 2 (b) y = f(x - 1) + 2 (c) y = 2 f(-x) (-1.2) (-2,-1) y = f(x) (3, 1)
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(2x) (b) y = f(x) - (c) y = 2f(1 x) 3 - 1 23 - y = f(x) 23
Solve the equation or inequality. (a) x²-3x + 2 = 0 (c) x²-3x+2>0 (b) x²-3x + 2
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(2x) + 1 (b) y = 2 f(x) + 1 (c) y = f(2-x) I 3 P 1 L y = f(x)
Solve the equation 2x2 - 3y2 = 6 for y. Is y a function of x?
Find all complex solutions. 2x² + 3 = 2x
Use the graph of y = f(x) to solve the inequality. Use interval notation to express your answer. (a) f(x) > 0 2 7 (b) f(x) = 0 y = f(x)
Solve h = -(1/g)t2 + 100 for t.
Find all complex solutions. 4x² +9=0
Solve the inequality. Use set-builder or interval notation to write the solution set to the inequality. x²-3x + 2 ≤0
Solve the inequality. Use set-builder or interval notation to write the solution set to the inequality. n(n-2) 15
Solve the inequality. Use set-builder or interval notation to write the solution set to the inequality. 9x²-4>0
Solve the inequality. Use set-builder or interval notation to write the solution set to the inequality. n²² +4 ≤ 6n
Write the requested equation. Then graph the given equation and your equation. Reflect f(x) = V-x + 1 across the y-axis.
Sketch a graph of f(x) = ax2 + bx + c that satisfies that given conditions. a < 0, b² - 4ac = 0
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis. f(x)=4-7x - 2x²
Sketch a graph of f(x) = ax2 + bx + c that satisfies that given conditions. a < 0, b² - 4ac < 0
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis. f(x) = x² - 2x - 3
Write the requested equation. Then graph the given equation and your equation.Reflect f(x) = |x| 1 across the x-axis.
Sketch a graph of f(x) = ax2 + bx+c that satisfies that given conditions. a> 0, b² - 4ac < 0
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis. f(x) = x + 1-1
Write the requested equation. Then graph the given equation and your equation.Reflect f(x) = √x + 1 across the x-axis.
Use the given graph of y = f(x) to sketch a graph of each expression. (a) y = f(x + 1) - 2 (b) y = -2f(x) (c) y = f(2x) (-2, 1) -y = f(x) (2, 1) (0.-1)
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis. f(x) = |x-2 +2
Write the requested equation. Then graph the given equation and your equation.Reflect f(x) = x2 - x across the y-axis.
Sketch a graph of f(x) = ax2 + bx + c that satisfies that given conditions. a < 0, b² - 4ac >0
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis.Line graph determined by the table X f(x) -1 -4 0 2 1 2
Sketch a graph of f(x) = ax2 + bx+c that satisfies that given conditions. a> 0, b² - 4ac > 0
For the given representation of a function f. graph the reflection across the x-axis and graph the reflection across the y-axis.Line graph determined by the table f(x) 2 -1 3 1 -1 2 -2
If f(x) = 2x2 - 3x + 1, use transformations to graph y = -f(x) and y = f(-x).
Sketch a graph of f(x) = ax2 + bx+c that satisfies that given conditions. a> 0, b² - 4ac = 0
Use transformations to sketch a graph of f. f(x) = x² - 4
Use transformations to sketch a graph of f. f(x) = -4√-x
Suppose that the graph of y = f(x) increases on an open interval (a, b). Answer the following.Does the graph of y = -f(x) increase or decrease on the interval (a, b)?
Suppose that the graph of y = f(x) increases on an open interval (a, b). Answer the following.Does the graph of y = f(-x) increase or decrease on the interval (-b, -a)?
Suppose that the graph of y = f(x) increases on an open interval (a, b). Answer the following.Does the graph of y = -f(-x) increase or decrease on the interval (- b, -a)?
Suppose that the graph of y = f(x) increases on an open interval (a, b). Answer the following.If c > 0, does the graph of y = -cf(x) increase or decrease on the interval (a, b)?
Use transformations to sketch a graph of f. f(x) = -2(x - 2)² + 3
Complete the following. (a) Use the vertex formula to find the vertex. (b) Find the intervals where f is increasing and where f is decreasing. f(x) = -x²+x-3
Use transformations to sketch a graph of f. f(x) = -x - 3|
A slingshot is used to propel a stone upward so that its height h in feet after / seconds is given by h(t) = -16t2 +88t + 5. (a) Evaluate h (0) and interpret the result. (b) How high was
Evaluate the expression with a calculator. (-12.6-5.7i)(5.1-9.3i)
The revenue R in dollars received from selling x radios is R(x) = x(90 - x). (a) Evaluate R (20) and interpret the result. (b) What number of radios sold maximize revenue? (c) What is
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = (x − 3)² + 1
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = (x + 2)² - 3
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). (1 + x)² = (x)ƒ
The function given by the formula f(x) = 0.000478x2 - 1.813x + 1720.1 models world population in billions from 1950 to 2020 during year x. (a) Evaluate f(1985) and interpret the
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = 2(x-4)²
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x)=-x-3
A homeowner has 44 feet of fence to enclose a rectangular garden. One side of the garden needs no fencing because it is along the wall of the house. What dimensions will maximize area?
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x)=√x+5
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = 2√-x
A box is being constructed by cutting 3-inch squares from the corners of a rectangular sheet of metal that is 4 inches longer than it is wide. If the box is to have a volume of 135 cubic inches, find
Room prices are regularly $100, but for each additional room rented by a group, the price is reduced by $3 for each room. For example, 1 room costs $100, 2 rooms cost 2 * $97= $194, and so
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). x/\ = (o)/
The following table gives estimates for the total number of minutes in billions spent on Facebook per year. Find a function in the form M(x) = a(x - h)2 + k that models this data. Year 2007 Minutes
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = -(x + 1)]
The table shows how irrigation of rice crops affects yield, where x represents the percent of total area that is irrigated and y is the rice yield in tons per hectare. (1 hectare ≈ 2.47 acres.)(a)
Use transformations to explain how the graph off can be found by using the graph of y = x2, y = √x, or y = |x|. You do not need to graph y = f(x). f(x) = |4 − x|
Use transformations to sketch a graph of f. f(x) = x² - 3
Use transformations to sketch a graph of f. f(x) = -x²
Use transformations to sketch a graph of f. f(x) = -√x
Use transformations to sketch a graph of f. f(x) = (x - 5)² + 3
Use transformations to sketch a graph of f. f(x) = (x + 4)²
Use transformations to sketch a graph of f. f(x) = |x|- 4
Use transformations to sketch a graph of f. f(x)=√x - 3+2
Use transformations to sketch a graph of f. f(x) = 2(x - 1)² + 1

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