Functions Precalculus

Information about a function g(x) is given in the table. The function g(x) is defined for all real numbers. Find the average rate of change of g(x) on the interval [-2, 4].

• 2

• 3

• 4

• 5

Information about a function $ g(x) $ is given in the table. The function $ g(x) $ is defined for all real numbers. Which of the following statements is guaranteed to be true about $ g(x) $?

• $ g(x) $ has a relative maximum at $ x = -2 $.

• $ g(x) $ has a relative minimum at $ x = 4 $.

• $ g(x) = 0 $ for some $ x $ in the interval $[-2, 4]$.

• The range of $ g(x) $ is $(- \infty, 11]$.

Which of the following equations could represent the graph shown?

• I only

• I and III

• II and IV

• I, II, and IV

• A.
• B.
• C.
• D.

Consider the function f(x) = 2 + √(x + 5). What is the range of f(x)?

• [2, ∞)

• [0, ∞)

• (-∞, ∞)

• [5, ∞)

Identify the transformations that occurred from the parent function y = x³ to produce the graph of f(x) =-(x + 2)³ .

• Reflection over the x-axis and horizontal shift left by 2 units

• Vertical stretch and horizontal shift right by 2 units

• Reflection over the y-axis and vertical shift up by 2 units

• Horizontal compression and vertical shift down by 2 units

Ellie manages her mom’s online candle business, Cathy’s Candles, and is responsible for setting prices that will maximize revenue, . The equation R(c)=(500-5c)(c-4) models the total revenue earned when { c } dollars is charged for one candle. a: find R(7) and interpret in the context of this problem b: How much can Cathy's Candles charge before revenue starts decreasing?

The function below can be used to model the height (h, in feet) of a ball t-seconds after it is launched into the air. What is the height of the ball once 5 seconds have passed?

h(t) = -16t² + 75t + 80

• 55 feet

• 124 feet

• 375 feet

• 535 feet

What is f(1)?

• 6

• -2

• sqrt(2)

• Undefined

What is the domain of the for the following piecewise function?