Question 1

Suppose the graph of a function $$f is $$known. Then the graph of $$y = f(x - 2)$$ may be obtained by a _____ shift of the graph of $$y = f(x) a $$distance of 2 units.

Accepted Answer

horizontal right

Question 2

Suppose the graph of a function $$f is $$known. Then the graph of $$y = -f(x)$$ may be obtained by a reflection about the _____ axis of the graph of $$y = f(x).$$

Accepted Answer

x

Question 3

Determine whether the following statement is true or false: The graph of $$y = 6f(x) is $$the graph of $$y = f(x)$$ vertically stretched by a factor of 6.

Accepted Answer

True, because the graph of the new function is obtained by multiplying each y-coordinate of $$y = f(x) by 6.$$

Question 4

Reflecting a function $$y = f(x)$$ across the x-axis involves multiplying $$f(x) by $$which value?

Accepted Answer

$$-1$$, giving $$y = -f(x)$$

Question 5

Which of the following functions has a graph that is the graph of $$y = \sqrt{x}$$ shifted up 1 unit?

Accepted Answer

$$y = \sqrt{x} + 1$$

Question 6

Write the function whose graph is the graph of $$y = |x|$$ but is shifted to the right 6 units.

Accepted Answer

$$y = |x - 6|$$

Question 7

Write the function whose graph is the graph of $$y = x^2$ but is shifted up 2 units.

Accepted Answer

$$y = x^2$ + 2$$

Question 8

Write the function whose graph is the graph of $$y = 3\sqrt{x}$$ but is reflected about the y-axis.

Accepted Answer

$$y = 3\sqrt{-x}$$

Question 9

Write the function whose graph is the graph of $$y = \sqrt{x}$$ but is vertically stretched by a factor of 8.

Accepted Answer

$$y = 8\sqrt{x}$$

Question 10

Find the function that is finally graphed after the following transformations are applied to the graph of $$y = \sqrt{x} in $$the order listed: (1) Shift up 7 units, (2) Shift left 2 units, (3) Reflect about the y-axis.

Accepted Answer

$$y = \sqrt{-x + 2} + 7$$

Question 11

Find the function that is finally graphed after the following transformations are applied to the graph of $$y = \sqrt{x} in $$the order listed: (1) Reflect about the x-axis, (2) Shift down 4 units, (3) Shift right 6 units.

Accepted Answer

$$y = -\sqrt{x - 6} - 4$$

Question 12

Find the function that is finally graphed after the following transformations are applied to the graph of $$y = \sqrt{x} in $$the order listed: (1) Vertical stretch by a factor of 3, (2) Shift up 4 units, (3) Shift right 5 units.

Accepted Answer

$$y = 3\sqrt{x - 5} + 4$$

Question 13

Which transformation of $$y = x^4$ results in the function f(x) = (x$$ + $$4)^4$$?

Accepted Answer

A horizontal shift 4 units left

Question 14

Which transformation of $$y = x^2$ results in the function f(x$$) = $$x^2 - 8$?

Accepted Answer

A vertical shift 8 units down

Question 15

Which transformation of $$y = \frac{1}{x}$$ results in the function $$f(x) = \frac{2}{x}$$?

Accepted Answer

A vertical stretch by a factor of 2

Question 16

Which transformation of $$y = x^3$ results in the function h(x$$) = $$-x^3$$?

Accepted Answer

Reflection about the x-axis

Question 17

Which graph shown below is the graph of the function $$f(x) = x^2$ - 6$$?

Accepted Answer

A parabola opening upward, vertex at $$(0, -6)$$

Question 18

Match the function $$f(x) = x^2$ - 4x + 3 to $$one of the given graphs.

Accepted Answer

A parabola opening upward, vertex at $$(2, -1)$$, x-intercepts at $$x = 1$$ and $$x = 3$$

Question 19

Match the function $$f(x) = x^2$ - 6x to $$one of the given graphs.

Accepted Answer

A parabola opening upward, vertex at $$(3, -9)$$, x-intercepts at $$x = 0$$ and $$x = 6$$

Precalculus Practice: Graph Transformations and Function Operations

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