Week 3 Quiz

On the curve x = y², the input x = 4 pairs with the outputs y = 2 and y = −2. Which statement about x = y² is true?

Select one.

• It is a function of x, because 2 and −2 both square to 4
• It is not a function of x, because the input 4 has two outputs
• It is a function of x, because a horizontal line meets it only once
• It is not a function of x, because two inputs share one output

Let p(x) = x² and q(x) = x + 1. Then (p ∘ q)(2) = 9 and (q ∘ p)(2) = 5, so changing the order of a composition can change the result.

True or false.

• True
• False

Let f(x) = 3x² − 2x + 5. Find f(−2). Enter a whole number only.

Type a short answer.

A student evaluates f(x) = 3x² − 2x + 5 at x = −2 and writes 3(−4) + 4 + 5 = −3. Which step went wrong?

Select one.

• The square: (−2)² is +4, so the first term should be 3 · 4 = 12
• The middle term: −2(−2) should be −4, not +4
• The constant: the 5 should be subtracted, not added
• Nothing went wrong: f(−2) is −3

A bowl shop charges g(x) = 3x + 4 dollars for x toppings. A friend orders 2 more toppings than you, and you order a toppings. Which expression is g(a + 2)?

Select one.

• 3a + 6
• a + 6
• 3a + 10
• 6a + 4

Let f(x) = 3x² − 2x + 5. Which expression is f(−x)?

Select one.

• −3x² + 2x + 5
• 3x² − 2x + 5
• −3x² − 2x + 5
• 3x² + 2x + 5

What is the domain of s(x) = √(x − 5)?

Select one.

• [5, ∞)
• (5, ∞)
• (−∞, 5]
• [−5, ∞)

Let r(x) = (x + 1) ⁄ (x − 3) and s(x) = √(x − 5). Select every true statement.

Select every option that applies.

• The input 3 is left out of the domain of r
• The input −1 is left out of the domain of r
• The input 5 is in the domain of s
• The input 4 is in the domain of s
• The domain of r is (−∞, 3) ∪ (3, ∞)

A launched object's height in feet is h(t) = −16t² + 64t + 80. Its heights at t = 0, 1, 2, 3, 4, 5 seconds are 80, 128, 144, 128, 80, 0, and it lands at t = 5. On the domain [0, 5], what is the range of h?

Select one.

• [0, 5]
• [0, 144]
• [80, 144]
• [0, 2]

Let f(x) = 3x² − 2x + 5 and g(x) = 3x + 4. Which expression is (f − g)(x)?

Select one.

• 3x² − 5x + 9
• 3x² + x + 9
• 3x² − 5x + 1
• 3x² − 2x + 1