When we work with functions, we use a very specific notation to ask for the function's value given a certain input for the independent variable. Additionally, we will be looking at two new scenarios: adding/subtracting two polynomial functions and multiplying/dividing two polynomial functions.

Test Objectives
• Demonstrate the ability to use function notation
• Demonstrate the ability to add/subtract polynomial functions
• Demonstrate the ability to multiply/divide polynomial functions
Operations on Functions Practice Test:

#1:

Instructions: Perform each indicated operation.

a) $$g(x)=-5x^3 - 7x + 1$$ find: $$g(0),~g(-1), ~g(-3)$$

#2:

Instructions: Perform each indicated operation.

a) $$f(x)=7x^3-9x+4$$ $$h(x)=12x^3 + 6x$$ $$g(x)=-19x^3 + 2x^2 - 5$$ find: $$(f + h + g)(x)$$ $$(f + h + g)(-2)$$

#3:

Instructions: Perform each indicated operation.

a) $$f(x)=-5x^3-13x^2+2x-12$$ $$g(x)=5x^3 - x^2 - 13x$$ $$h(x)=-9x^3 - 10x^2 + x + 10$$ find: $$(f - g - h)(x)$$ $$(f - g - h)(-1)$$

#4:

Instructions: Perform each indicated operation.

a) $$f(x)=3x$$ $$g(x)=6x - 6$$ $$h(x)=7x + 4$$ find: $$(fgh)(x)$$ $$(fgh)(-1)$$

#5:

Instructions: Perform each indicated operation.

a) $$f(x)=7x^3 - 24x^2 + 16x - 21$$ $$g(x)=x - 3$$ find: $$\left(\frac{f}{g}\right)(x)$$ $$\left(\frac{f}{g}\right)(-5)$$

Written Solutions:

#1:

Solutions:

a) $$g(0)=1$$ $$g(-1)=13$$ $$g(-3)=157$$

#2:

Solutions:

a) $$(f + g + h)(x)=2x^2 - 3x - 1$$ $$(f + g + h)(-2)=13$$

#3:

Solutions:

a) $$(f - g - h)(x)=-x^3 - 2x^2 + 14x - 22$$ $$(f - g - h)(-1)=-37$$ $$(f - g - h)(x)=$$$$-x^3 - 2x^2 + 14x - 22$$ $$(f - g - h)(-1)=-37$$

#4:

Solutions:

a) $$(fgh)(x)=126x^3 - 54x^2 - 72x$$ $$(fgh)(-1)=-108$$

#5:

Solutions:

a) $$\left(\frac{f}{g}\right)(x)=7x^2 - 3x + 7$$ $$\left(\frac{f}{g}\right)(-5)=197$$