Mathematics Quiz

For 𝑓(𝑥) = √𝑥 − 6, what is the vertex of 𝑓(𝑥) after being horizontally dilated by a factor of 2? Write your answer as an ordered pair. Do not include spaces.

Answer explanation

(3,0)

If the absolute value child function 𝑔(𝑥) has a 𝑦-intercept at (0, 5), where is the 𝑦-intercept of 𝑔 (1/2x)?

• (0, 2.5)

• (0, 5)

• (0, 10)

• There is no y-intercept.

Let 𝑟(𝑥) = 1/(𝑥+8). This function has a vertical asymptote at 𝑥 = −8. What is the equation of the vertical asymptote of 𝑟(−8𝑥)? Do not include spaces in your response.

Answer explanation

x=1

What is the only parent function that looks exactly like its inverse?

• Linear

• Rational

• Absolute Value

• Logarithmic

A function 𝑓(𝑥) includes the points (2, 3), (–5, 1), and (10, –3) in its graph. Based on this, which of the following points must be included in the graph of 𝑓−1(𝑥)? Choose TWO correct answers.

• (–3, 10)

• (3, 2)

• (3, 4)

• (–1, 5)

• (–3, –2)

Which of the following is the inverse of 𝑦 = (𝑥 − 3)³?

• 𝑦 = 𝑥 − 3 ³

• 𝑦 = 𝑥 + 3 ³

• 𝑦 = ∛ x− 3

• 𝑦 = ∛ x+ 3

A logarithmic child function has domain of (−2, ∞). What is the range of the exponential child function that is its inverse?

• (−2, ∞)

• (2, ∞)

• (−∞, −2)

• (−∞, 2)

The grid shows 𝑓(𝑥), an exponential child function, and 𝑓−1(𝑥), the logarithmic child function that is its inverse. Graph the line over which 𝑓(𝑥) is reflected to create the graph of 𝑓−1(𝑥).

What is the domain of the cubic parent function after being horizontally stretched by a factor of 3?

• x∈ℝ

• (−∞, 0) ∪ (0, ∞)

• {𝑥|3𝑥 ≥ 0}

• [0, ∞)

Which of the following graphs depicts a one-to-one function?

• A

• B

• C

• D