Graphs of Combinations of Functions
Sum/ Differences of Functions
Product/ Quotient of
Functions
Functions
Composition of
Functions
Functions
Application
Problems
Problems
100
Graph the following: x2 + sqrt{x+4}
100
Determine the equation for H(x) = F(x) + G(x) and state the domain and range.
F(x) = 5x +2 G(x) = 6
H(x) = 5x + 8
Domain = (XER)
Range = (YER)
100
f(x) = x^2 + 7 and g(x) = x + 5. Determine (f x g).
(f x g) = x^3 + 5x^2 + 7x + 35
100
f(x) = x^2 + 5 and g(x) = -6x. Determine f(g(x) and state the domain of f(g(x)
f(g(x) = 36x^2 + 5
Domain = (XER)
100
A car shop has an ongoing sale discount for any modeled by the function f(x)= 0.64x, If you have a coupon with a discount modeled by the function g(x)= x-1300. Determine the equation that represents the total discount. Assume that the sale discount is applied first.
0.64x-1300
200
Match the graph with the equation:
a) 3sinx-cos3x
b) sqrt{x+4}+cos2x
c)sinx+log(x+8)
d)x2 4cosx
c)
200
Determine the equation for H(x) = F(x) + G(x) and state the domain of H(x).
F(x) = 2x^2 - 3x + 1 G(x) = x^2 - x - 6
H(x) = 3x^2 - 4x - 5
Domain = (XER)
200
Given f(x) = x^2 + 9 and g(x) = 2x + 5. find (f x g) (x) and determine ( f x g) (12)
( f x g) = 2x^3 + 5x^2 + 18x + 45
( f x g) (12) = 4437
200
f(x) = x^2 - 8 and g(x) = 3x. Determine f(g(x), g(f(x) and state the domain of f(g(x) and g(f(x)
f(g(x) = 9x^2 - 8
g(f(x) = 3x^2 - 24
Domain f(g(x) = (XER)
Domain g(f(x) =(XER)
200
For a car traveling at a constant speed of 65 km/h, the distance driven, 𝒅, in kilometers, is represented by 𝒅(𝒕) = 65𝒕, where 𝒕 is the time in hours. The cost of gasoline, in dollars, for the drive is represented by 𝑪(𝒅) = 𝟎. 𝟎𝟗d. Determine the cost of gasoline after 8 hours of driving.
$46.8
300
Create the graph of both (f+/-g) (x) and (f)(x), g(x).
300
f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1. Find the (f+g) (x) and (f-g) (x)
(f+g) (x) = 5x^2 + 6x - 1
(f-g) (x) = x^2 + 8x + 1
300
f(x) = 1/x^2 - 5x - 14 and g(x) = secx. Determine the equation for f(x)g(x) and state the domain.
(f x g) (x) = secx/x^2 - 5x - 14
D: ( x ≠ -2.7, pi/2, XER )
300
If f(x) = 2√ (x) and g(x)= x-9. Determine f(g(x)) and state the domain
f(g(x)) = 2√ (x-9)
D:(x>=9,XER)
300
The price of x number of bags of chips at the grocery store in dollars is represented by the function f(x)= 2x. If there is a 13% tax, Write an equation that represents the total cost.
h(x) = 2x+2(0.13x)
h(x) = 2.26x
400
Using (f)(x) and g(x) graph them and create another graph of (f+g)(x) :
(f+g)(x)
400
if f(x) = x2+7x+3 and g(x) = 2x+8. Determine
(f + g-1) (x)
(f + g-1) (x)=x2+7.5x-1
400
f(x) = 2sinx and g(x) = cosx. Determine the product and quotient of the functions and state the domain.
product f(x) = sin2x
Domain = (XER)
quotient f(x) = 2tanx
Domain = (XER/ X ≠pi/2, 3pi/2, 5pi/2)
400
If f(x)= 7x+12 and g(x) = 3x-4. Determine
f(g-1(x)) and state the domain.
f(g-1(x))= (7x+64)/3
D:(XER)
400
The function, 𝑪(𝑭) = 𝟓/𝟗 (𝑭 − 𝟑𝟐) relates the temperature in degrees Celsius and the temperature in degrees Fahrenheit. The function 𝑲(𝑪) = 𝑪 + 𝟐𝟕𝟑. 𝟏𝟓 relates the temperature in degrees Celsius and the Kelvin temperature.
What is 40°F in Kelvin?
277.59K
500
Graph the following f(x) and g(x) and (f+g)(x).
500
Given f(x)= x2-nx+5 and g(x)= mx2+x-, determine the values of n and m if the points (1,3) and (-2,18) satisfy the function h(x)=f(x)+g(x).
n=3
m=2
500
if f(x)= (3x)/(x+4), g(x)= (x+7)/(x-4) and h(x) = (-x)/x. Determine (f x g x h)(x) and evaluate (f x g x h)(3)
(f x g x h)(x) = -((3x2+21x)/(x2-16))
(f x g x h)(3) = 12.857
500
if f(x) = 3x+4, g(x)= 8x2+7 and h(x) = 7x+2. Determine f(g(h(x))) and state the domain and range.
f(g(h(x)))= 1176x2+672x+121
D:(XER)
R:(Y>=25,YER)
500
A store is having a sale where all items are 23% off(f(x)). Yesterday, you obtained a coupon for $13(g(x)) off any item in the store. Assume that the sale discount is applied first, determine an equation that represents the total discount where x represents the original price of the item. Then, determine the equation that represents the total discount if the coupon discount is applied first. Which method offers a better discount?
g(f(x)) = 0.77x-13
f(g(x))0.77x-10.01
Sale discount first