Question 1

Which transformation will shift the graph of $$y = f(x)$$ three units down?

Accepted Answer

$$y = f(x) - 3$$

Question 2

Given $$f(x) = x^2$, which equation represents the graph of f(x$$)$$ shifted 4 units to the left and 2 units up?

Accepted Answer

$$y = (x + 4)^2$ + 2$$

Question 3

If $$g(x) = -f(x)$$, what transformation has been applied to $$f(x)$$?

Accepted Answer

Reflection about the x-axis

Question 4

Which of the following describes the transformation from $$y = |x| to$$ $$y = 2|x|$$?

Accepted Answer

Vertical stretch by a factor of 2

Question 5

Given $$f(x) = x^2$, what is the effect of the transformation y = f(2x$$)$$?

Accepted Answer

Horizontal compression by a factor of 2

Question 6

Which sequence of transformations will produce $$y = -|x + 1| + 4$$ from $$y = |x|$$?

Accepted Answer

Shift left 1, reflect about x-axis, shift up 4

Question 7

If $$f(x) = (x + 2)^2$ - 5$$, what is the vertex of the parabola?

Accepted Answer

(-2, -5)

Question 8

A function $$f(x) is $$reflected about the y-axis. Which equation represents this transformation?

Accepted Answer

$$y = f(-x)$$

Question 9

Given $$f(x) = x^2$, which transformation results in y = -3(x$$ - $$2)^2 + 1$?

Accepted Answer

Shift right 2, vertical stretch by 3, reflect about x-axis, shift up 1

Question 10

Suppose $$f(x) = |x|. $$What is the graph of $$y = |f(x)|$$?

Accepted Answer

The same as $$y = |x|$$

Question 11

A real-world application: The velocity of blood flow in an artery is given by $$v(r) = c(R^2$ - r^2$). If$$ $$R = 3$$ and $$c = 104$$, what is the maximum velocity?

Accepted Answer

$$9 \cdot 104$$

Question 12

Which transformation will change the graph of $$y = f(x) so $$that all negative $$y-$$values are reflected above the x-axis?

Accepted Answer

$$y = |f(x)|$$

Question 13

Given $$f(x) = \sqrt{x}$$, what is the domain of $$g(x) = \sqrt{x + 2} - 3$$?

Accepted Answer

$$x \geq -2$$

Question 14

If $$f(x) = |x|$$, which transformation results in $$y = \frac{1}{2}|x|$$?

Accepted Answer

Vertical compression by a factor of $$\frac{1}{2}$$

Question 15

Which transformation will shift the graph of $$y = f(x)$$ two units to the right?

Accepted Answer

$$y = f(x - 2)$$

Question 16

Given $$f(x) = x^2$, what is the effect of the transformation y = f$$(\frac{1}{2}x)$$?

Accepted Answer

Horizontal stretch by a factor of 2

Question 17

Which of the following is the correct sequence to graph $$y = -2(x + 1)^2$ + 5$$ starting from $$y = x^2$?

Accepted Answer

Shift left 1, stretch vertically by 2, reflect about x-axis, shift up 5

Question 18

If $$f(x) = x^2$, which transformation results in y = f(-x$$)$$?

Accepted Answer

Reflection about the y-axis

Question 19

Given $$f(x) = x^2$, what is the range of g(x) = f(x) - 4$?

Accepted Answer

$$[-4, \infty)$$

Transformations of Functions: Precalculus Study Guide

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