PC L 47 Combining Functions

Lesson 47 - Combinations (Adding or Subtracting) of Functions REVIEW

Objective

■ To be able to perform

operations and
combinations of functions
algebraically, graphically.

Relevance

■To be able to model a

set of raw data after a
function to best
represent that data.

Operations with Functions:

■ Sum

■ Difference

■ Product

■ Quotient

Example: Let f(x) = 5x² -2x +3 and
g(x) = 4x² +7x -5

■ Find f + g
■ Find f - g

Example:

Example: Let f(x) = 5x² and
and g(x) = 3x – 1.

■ Find f · g
■ Find f/g

Example:

Example: f(x)=2x + 3 and g(x) = x -7

Multiple Choice

Simplify by combining like terms:

5a + 2b - 3a + 4

• 8a + 2b + 4

• 2a + 2b + 4

• 8ab

• 4ab + 4

Multiple Choice

What is the domain of the graph?

• [-7, 5)

• (-7, 5]

• [-3, 1)

• (-3, 1]

Multiple Choice

What is the range of the function?
Hint:  Graph counts by 2's.

• (-∞, ∞)

• (0, 3)

• (0, 15)

• (3, 15)

Multiple Choice

Given

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,

find (f + g)(x).

• 11x² - 1

• 5x⁴ + 6x² - 1

• 5x² + 6x - 1

• 5x² + 8x - 1

Multiple Choice

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,

find (f - g)(x).

• x² + 8x + 1

• x² + 6x - 1

• 5x² + 8x - 1

• x² + 8x -1

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x). 

• 14x-10

• -8x+2

• 2x+2

• 2x-2

Multiple Choice

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x). 

• x²+x+9

• x²-x+9

• x²-x

• x²-x+18

Multiple Choice

When f(x) = 4x+8 and
g(x) = x+3, find
f(x) * g(x). 

• 4x²+24

• 4x²+20x+24

• 4x²+12x+24

• 4x²+4x+24

Multiple Choice

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

• 5n+1

• -5n+1

• -2n+1

• -6n-1

Multiple Choice

f(x)=2x+4
g(x)=3x²-1
Find f(x)*g(x)

• 6x⁴+12x³-4x²-8x

• -6x³+12x²+2x-4

• 6x³+12x²-2x-4

• 5x²-18x+20

Multiple Choice

h(x) = 3x + 3

g(x) = -4x + 1

Find (h + g)(10)

hint: add h(x) and g(x), then plug in 10

• -6

• 6

• 82

• -72

Multiple Choice

Find (f + g)(x)

• 2x² - 3

• 9

• x⁴ - 3x² - 18

• (x² + 3)/(x² -6)

Multiple Choice

Given the graphs of H and K, describe the domain of H + K.

• All real numbers

• [-4 , -3) ∪ (-3, 3) ∪ (3, 3.5]

• [-3, 3]

• [-4, 2.5]

Multiple Choice

Find the domain of

$$f\left(x\right)=\sqrt{x+3}$$  

• $$-3\le x<\infty$$  

• $$-\infty<x\le-3$$  

• $$3\le x<\infty$$  

• All Real Numbers

Multiple Choice

What number CANNOT be in the denominator of a fraction?

• a negative number

• 0

• 1

• any whole number

Multiple Choice

Let f be the linear function (in blue) and let g be the parabolic function (in red). Find $$g\left(f\left(2\right)\right)$$  

• 0

• 2

• -2

• 4