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college algebra graphs and models

College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions

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 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) = 2x²-3x + 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 left 8 units and downward 5 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. 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) Shifted left 2 units, reflected about the y-axis
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 right 1 unit and upward 10 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 3x + 2 (a) Shifted right 2000 units and upward 70 units (b) Shifted left 300 units and downward 30 units
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 left 5 units and upward 2 units
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) Reflected about the y-axis, shifted right 3 units
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 the stone after 2 seconds? (c) Find the maximum height of the stone. (d) At what time(s) 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 the maximum revenue? (d) What number of radios should be sold for rev- enue to be $2000 or more?
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 result. (b) Estimate world population during the year 2000. (c) According to this model, when did
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 the dimensions of the metal sheet.
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 on. (a) Write a quadratic function C that gives the total cost of renting x rooms. (b) What is 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). 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 60 2008 84 2009 184 2016 2500
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 least-squares regression to find a quadratic function that models the data. (b) Solve 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) = |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
Use transformations to sketch a graph of f. f(x) = -√1-x
Use transformations to sketch a graph of f. f(x) = -x² + 4
Use transformations to sketch a graph of f. x-^ = (x)f
Use transformations to sketch a graph of f. f(x) = |2x|

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