Linear Equations, Graphs of Functions, Operations on Functions, Difference Quotient

Linear Equations

300

Find the equation of the line passing through (-1,-5) and perpendicular to y = -1/4 x + 2

y = 4x - 1

400

Find the equation of a line passing through (6, -1) and parallel to x - 2y = -4

y = 1/2 x - 4

500

Find the secant line

f(x)= -3x²+4x from x₁=-1 and x₂=2

y = x - 6

Analyzing Graphs of Functions

200

Identify its domain and range.

Domain : [-2,1)

Range: [1,5]

300

https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=emm_epm0_pte_nus_dpg&f=a

Determine the intervals for the period from 2016 through 2022 over which the function is increasing, decreasing, or constant.

increasing [2016, 2018] , [2020, 2022]

decreasing [2018, 2020]

400

Identify its domain and range

Domain (-infinity, 4]

Range [0, infinity)

500

Describe transformation of the function.

reflected across the x-axis

shifted 1 units left.

shifted 4 units up.

Combinations of Functions

300

Let f(x) = 2x² + 17x + 21         g(x) = x + 7

find (f/g)(x) and (f - g)(x)

2x + 3 

2x² + 16x + 14

400

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

find (fg)(x) and (f/g)(x)

2x³ + x² - 4x - 3

2x - 3

Composition of Functions

200

Given f(x) = -12x + 7 and g(x) = 3x² - 8x + 2

find (f o g)(x)

-36x² + 96x - 17

300

Given f(x) = 3x - 1 and g(x) = 5x² - 9x, 

find (g o f)(x)

45x² - 57x + 14

400

Given   f(x) = 5x - 2  and  g(x) = 2x² - 4x + 1, find 

(g o f)(x)

50x² - 60x + 17

Difference Quotient of a Function

200

Find the difference quotient of the function:

f(x) = 5x + 13

5

500

Find the difference quotient of the function: 

f(x) = 3x² - 2x + 5

6x + 3h - 2