Question 1

Given the function $$f(x) = x^2$, what is the range of the function g(x$$) = $$x^2 - 4$ after applying a vertical shift down by 4 units?

Accepted Answer

$$[-4, \infty)$$

Question 2

What is the domain of the function $$g(x) = x^2$ - 4$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

If $$f(x) = x^2$ and g(x$$) = $$x^2 + 3$, how does the graph of g(x$$)$$ compare to f(x$$)$$?

Accepted Answer

It is shifted 3 units up.

Question 4

Which of the following statements about vertical shifts is TRUE?

Accepted Answer

A vertical shift affects only the range of a function.

Question 5

If $$f(x) = x^2$ and h(x$$) = $$x^2 - 7$, what is the minimum value of h(x$$)$$?

Accepted Answer

$$-7$$

Question 6

Suppose $$f(x) = x^2$ and k(x$$) = $$x^2 + c$ for some constant c$. Which of the following describes the effect of increasing c$?

Accepted Answer

The graph shifts upward.

Question 7

Given $$f(x) = x^2$ and g(x$$) = $$x^2 - 4$, which of the following is the correct range for g(x$$)$$?

Accepted Answer

$$[-4, \infty)$$

Question 8

If a positive real number $$k is $$subtracted from the output of a function $$f(x)$$, what happens to the graph?

Accepted Answer

It is shifted vertically down by $$k$$ units.

Question 9

For the function $$f(x) = x^2$, what is the effect of the transformation f(x) - 4$ on the vertex of the parabola?

Accepted Answer

The vertex moves 4 units down.

Question 10

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -5t^2$ + 20t + 2. If $$the entire graph is shifted down by 3 meters, what is the new equation?

Accepted Answer

$$h(t) = -5t^2$ + 20t - 1$$

Question 11

If $$f(x) = x^2$ and g(x$$) = $$x^2 + k$, which of the following is the range of g(x$$)$$ for k = -5$?

Accepted Answer

$$[-5, \infty)$$

Question 12

Which transformation results in the graph of $$f(x) = x^2$ being shifted vertically up by 6 units?

Accepted Answer

$$f(x) + 6$$

Question 13

If the range of $$f(x) = x^2$ is $$[0, \infty)$$, what is the range of f(x) - 10$?

Accepted Answer

$$[-10, \infty)$$

Question 14

A vertical shift of a function $$f(x) by$$ $$k$$ units up is represented by which equation?

Accepted Answer

$$f(x) + k$$

Question 15

If $$f(x) = x^2$ and g(x$$) = $$x^2 - 4$, which of the following statements is true?

Accepted Answer

The range of $$g(x) is$$ $$[-4, \infty).$$

Vertical Shifts of Functions: Domain and Range

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