EOC Functions & Modeling

EOC Functions & Modeling

by Darryl Padgett

What is a composite function?

• Can be thought of a series of operations

• One function is substituted into another function

• Often denoted as f(g(x)) or (f ∘ g)(x)

• Read as "f of g of x"

• It is an operation on functions

• You are multiplying f(x) and g(x) not substituting functions

Composite Functions Example

Multiple Choice

Which expression represents g(f(x)) if f(x) = 2x - 8 and g(x) = 4x

• 8x - 32
• 8x² - 32x
• 8x - 8
• 6x - 8

Multiple Choice

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

• 9x² - 6x + 1

• 3x - 1

• 3x² - 1

• 9x² - 1

Multiple Choice

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

• 7
• -2
• -9
• -10

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

• -42
• -26
• -18
• None of these.

Multiple Choice

In 2014, the cost to mail a letter was 49¢ for up to one ounce. Every additional ounce cost 21¢. Which recursive function could be used to determine the cost of a 3-ounce letter, in cents? 

• 𝑎₁ = 49;

  𝑎_𝑛 = 𝑎_𝑛−1 + 21 

• 𝑎₁ = 0;

  𝑎_𝑛 = 49(𝑎_{𝑛 − 1} ) + 21 

• 𝑎₁ = 21;

  𝑎_𝑛 = 𝑎_𝑛−1 + 49 

• 𝑎₁ = 0;

  𝑎_𝑛 = 21(𝑎_𝑛−1) + 49 

Multiple Choice

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

Describe the transformation from dotted to solid.

• f(x + 4)
• f(x - 4)
• f(x) + 4
• f(x) - 4

Multiple Choice

If the blue is f(x)=x^2, the red must be

• g(x) = (x+3)²

• g(x) = (x-3)²

• g(x) = x²+3

• g(x) = x²-2

Multiple Choice

-f(x) - 2

• reflection over y-axis, shift down 2

• reflection over y-axis, shift right 2

• reflection over x-axis, shift right 2

• reflection over x-axis, shift down 2

Multiple Choice

The height, ℎ, in feet, of an object thrown upward from a height of 144 feet is a function of time, 𝑡, in seconds. The height can be determined by the function ℎ(𝑡)=−16𝑡² + 128𝑡 + 144 . What is the height of the object at 3 seconds? 

• 144

• 384

• 432

• 672

Multiple Choice

The number of miles a car can be driven depends on the number of gallons of gas in its tank. The function m = 25g models a situation in which a car gets 25 miles per gallon. If the gas tank holds 20 gallons of gas, which inequality represents its range? 

• 0 ≤ 𝑔 ≤ 20 

• 0 ≤ 𝑚 ≤ 500 

• 𝑚 ≤ 500 

• 𝑔 ≤ 20 

Multiple Choice

Let 𝑓 be a function such that 𝑓(𝑥) = 2𝑥 − 4 is defined on the domain 2 ≤ 𝑥 ≤ 6. The range of this function is 

• −∞ ≤ 𝑦 ≤ ∞ 

• 0 ≤ 𝑦 ≤ 8 

• 0 ≤ 𝑦 ≤ ∞ 

• 2 ≤ 𝑦 ≤ 6 

Multiple Choice

Given that 𝑦 is a function of 𝑥, which of the following tables best represents a function?  Hint: Remember that each input must have a different output.

Multiple Select

The domain of the function 𝑓(𝑥) = −3𝑥 is restricted to the negative integers. (The domain is the x values). Which values are elements of the range? 

• -12

• -3

• 12

• 7

• 9

Multiple Choice

Sue hits a ball from a height of 4 feet. The height of the ball above the ground is a function of the horizontal distance the ball travels until it comes to rest on the ground. What is the maximum height that the ball travels?

• 0 feet

• 50 feet

• 100 feet

• 200feet

Fill in the Blanks

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Multiple Select

The function 𝑓(𝑥) = 4𝑥− 𝑥² is graphed in the

𝑥𝑦-coordinate plane as shown. 

Based on the graph of the function, which statements are true? Select ALL that apply. 

• f is increasing on the interval

  0 < 𝑥 < 2. 

• f is decreasing on the interval

  0 < 𝑥 < 2. 

• f is increasing on the interval

  2 < 𝑥 < 4. 

• f is decreasing on the interval

  2 < 𝑥 < 4. 

• f is increasing on the interval 𝑥 > 4. 

Multiple Select

The function 𝑓(𝑥) = 4𝑥− 𝑥² is graphed in the

𝑥𝑦-coordinate plane as shown. 

Based on the graph of the function, which statements are true? Select ALL that apply. 

• f(x) < 0 on the interval 𝑥 < 0. 

• f(x) < 0 on the interval 0 < 𝑥 < 2 . 

• f(x) $$\ge$$ 0 on the interval 0 < 𝑥 < 2 . 

• f(x) > 0 on the interval 2 < 𝑥 < 4 . 

• f(x) < 0 on the interval 𝑥 > 4 . 

Multiple Choice

A computer technician charges a one-time fee of $50 plus an additional $20 per hour of labor. If an equation is created to determine the technician's total charge, what does the $50 represent?  Hint: create an equation of the line.

• slope

• coefficient

• x-intercept

• y-intercept

Multiple Choice

What is the maximum height of the fire hose water?

• 4 feet

• 24 feet

• 41 feet

• 45 feet

Fill in the Blanks

Multiple Choice

The distance in miles, 𝑦, a bicyclist is from home after riding 𝑥 hours is represented by the equation 𝑦 = 8𝑥 + 7. What does the slope represent in this situation? 

• the number of hours it takes the bicyclist to ride 15 miles 

• the distance the bicyclist is from home when 𝑥 = 0 

• the steepness of the hill the bicyclist is climbing 

• the speed of the bicyclist 

Multiple Choice

Which is the graph of a linear function with a slope of 2 and a y-intercept at (0, 1)? 

Multiple Choice

What is the equation of the function represented by this table of values? 

• 𝑦 = 5𝑥+3 

• 𝑦 = 12𝑥+3 

• 𝑦 = 3∙5^𝑥 

• 𝑦 = 5∙3^𝑥 

Multiple Choice

Which expression represents the output of the n^th term? 

• 𝑛 + 2 

• 𝑛 + 11 

• 2n + 1

• 2n -1