Concept explainers
Graphing Transformations The graph of
(a)
(c)
(e)
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College Algebra
- The graph below shows transformations of the graph of f(x)=2x. What is the equation for the transformation?arrow_forwardThe graph of y = f(x) passes through (0, 1), (1, 3), and (2, 0). Through what three points will the graph of y = f(x + 2) – 1 pass? Describe, verbally, in order, the transformations in going from y = |x| to y = -2|x – 1| + 3.arrow_forwardBased on your knowledge of transformations, which of the equations represents the graph of g (x)? a. g(x) = 3-2 – 1 b. g(x) =-3x+2 +1 c. g(x) = -3-2 +1 d. g(x) = 32+2 – 1arrow_forward
- The graph of a function f is given. Sketch the graphs of the following transformations of f. y (a) y = f(5x)arrow_forward4. Sketch a graph of the function Describe the transformations to the graph of y = x³arrow_forwardDescribe the transformations that produce the graphs of g and h from the graph of f. f(x) = x³ (a) g(x) = (x-1)³ - 2 (b) h(x) = -(x+4)³ +3 (a) Describe the transformations that produce the graph of g from the graph of f. Choose the correct answer below. O A. Shift 1 unit to the right, shift 2 units down OB. Shift 1 unit down, shift 2 units to the right OC. Shift 1 unit to the left, shift 2 units up O D. Shift 1 unit up, shift 2 units to the left (b) Describe the transformations that produce the graph of h from the graph of f. Choose the correct answer below. OA. Shift 3 units to the left, reflect in the x-axis, shift 4 units up OB. Shift 3 units to the right, reflect in the y-axis, shift 4 units down OC. Shift 4 units to the left, reflect in the y-axis, shift 3 units down OD. Shift 4 units to the left, reflect in the x-axis, shift up 3 units H Q Searcharrow_forward
- Graph the function using a combination of transformations applied to the graph of the basic function. h(x) = Vx+ 4 - 5 (xz -4) y y 2 2 -10 -5 10 -10 -5 10 -2 -2 -4 -4 -6 -6 -8 -8 -1아 -10 y y 10 10 8 6 4 4 2 2 - 10 -5 10 - 10 -5 10 -2- 2.arrow_forwardGraph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflecting). [Hint: If necessary, write f in the form f(x) = a(x – h)² + k.] 10- 8- 6- f(x) = x² + 2x - 2 14- Which transformations are needed to graph the function f(x) = x² + 2x – 2? Choose the correct answer below. 2- -2 10 O A. The graph of y = x should be horizontally shifted to the right by 1 unit and shifted vertically up by 3 units. 10 -8 .6. -4 +2- O B. The graph of y = x? should be horizontally shifted to the right by 3 units and shifted vertically down by 1 unit. 4- O C. The graph of y = x² should be horizontally shifted to the left by 3 units and shifted vertically up by 1 unit. -8- D. The graph of y = x should be horizontally shifted to the left by 1 unit and shifted vertically down by 3 units. -10 Aarrow_forwardGraph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflecting). [Hint: If necessary, write f in the form f(x) = a(x - h)² + k.] 10- 8- f(x) = x² + 2x – 2 6- Which transformations are needed to graph the function f(x) = x2 + 2x - 2? Choose the correct answer below. 14 2- O A. The graph of y = x² should be horizontally shifted to the right by 1 unit and shifted vertically up by 3 units. -10 -8. -6. -4. -2 6. 8. 10 -2- O B. The graph of y = x² should be horizontally shifted to the right by 3 units and shifted vertically down by 1 unit. -4- OC. The graph of y =x? should be horizontally shifted to the left by 3 units and shifted vertically up by 1 unit. 6- -8 O D. The graph of y = x2 should be horizontally shifted to the left by 1 unit and shifted vertically down by 3 units. -10- Click the graph, choose a tool in the palette and follow the instructions to create your graph.arrow_forward
- The graph of a function fis given. Sketch the graphs of the following transformations of f. (а) у 3 (2х) y 1. y (b) y= f(1/2x) y y 11 y yarrow_forwardFunctions g, r and s are transformations of the graph of f. Write the equations for g(x), r(x) and s(x) in terms of f(x)arrow_forwardThe graph of the function f(x)=1x+4−14 is a transformation of the graph of the function g(x)=1x what shifts were donearrow_forward
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