Function Operations

Operations on Functions

by Shannon Berkner

Multiple Choice

For f(x) = 2x + 1 and g(x) = x² - 7, find (f + g)(x).

• x² + 2x + 8

• 2x² - 15

• 2x³ - 6

• x² + 2x - 6

Fill in the Blanks

If $\ f\left(x\right)\ =\ 3x-1\ and\ g\left(x\right)=x+4\$ ,find  $\left(f+g\right)\left(-2\right)$   

​To find the domain and range, graph the new equation on your device.

Multiple Choice

If $$f\left(x\right)=2x+1\ \ and\ \ g\left(x\right)=x^2-7$$ , find $$\left(f\ -\ g\right)\left(x\right)$$  

• x² - 2x - 8

• 2x² - 15

• -x² + 2x + 8

• -x² + 2x - 6

Multiple Choice

$$f\left(n\right)=x^2+1,\ g\left(n\right)=2x-5$$  

Find $$\left(f-g\right)\left(n\right)$$  

• x²-2x+6
• -x²+2x+4
• -x²-2x-6
• x²-2x-4

Multiple Choice

If f(x) = 3x - 2 and g(x) = 2x + 1, find (f - g)(x).

• x - 3

• 3 - x

• 5x - 1

• 5x - 3

​Determining Sums or Differences from Graphs

ex) (g - f)(-4) = ?

Find x = -4 and then observe the y-values for each graph at that point.

​In this case subtract g from f.

​(g - f)(-4) = 1 - 7 = ___

​

​Now try (f + g)(-5) =

Fill in the Blanks

What is the value of $\left(f+g\right)\left(4\right)$ ?

​Multiplying

Functions

Multiple Choice

f(x) = 4x + 8

g(x) = x + 3,

Find f(x) ⋅ g(x)

• 4x² + 24

• 4x² + 20x + 24

• 4x² + 12x + 24

• 4x² + 4x + 24

Multiple Choice

f(x) = 4x + 1 and g(x) = 4x - 3
Find f(x) * g(x)

• 16x² + 8x - 3
• 16x² - 8x + 3
• 16x² - 8x - 3
• 16x² - 16x - 3

Multiple Choice

f(x)=x³-3x
g(x)=-4x+1
Find f(x)*g(x)

• -4x³-5x²-3
• -4x³+2x²-3x
• -4x⁴+x³+12x²-3x
• -4x^4-x³+12x²⁺3x

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