Made with Math

Functions

100

evaluate for x:

y=25+4x if x=5

x=45

200

if g(m)=√m−4, solve g(m)=2

m=8

300

if f(x) = x² + 5, what is f(-2) and f(0)

f(-2)=9

f(0)=5

400

consider the relation

3r+2t=18

write the relationship as a function

r=f(t)

r=18-2t/3

r=-2/3t+6

500

write a function rule given the points:

(0,5);(1,6);(2,7);(-1,4)

y=x+5

Inverse Functions

100

find the inverse of f(x)=x³+9.

f^-1(x)=(x-9)³

200

give the inverse of the function f = {(4,7), (2,-3), (5,7),(1, 8)}

f^-1 = {(7,4), (-3,2), (7,5), (8, 1)}

300

find the inverse of the following function:

g(x)=(x+2)²

g^-1(x)=√x−2

400

Find the inverse of the function

f(x)=2+(x−4)^1/3

f^-1(x)=-(x-2)³+4

500

find the inverse of the function:

g(x)=2x/1-x

g^-1(x)=x/2+x

Polynomials

100

multiply the polynomials:

3x²(2x⁴)

6x⁶

200

simplify:

(3x³-5x+9)+(6x³+8x-7)

9x³+3x+2

300

evaluate the polynomials:

(d + 3)(d² - 4d + 1)

d³ - d² -11d + 3

400

simplify:

(5x³-7x²-8)-(4x²+5x-6)

5x³-11x²-5x-2

500

The volume of a rectangular solid is given by the polynomial 3x4−3x3−33x2+54x. The length and width of the solid are 3x and x−2. Find the height of the solid.

h=x²+x-9

Linear Functions

100

write a linear function with a slope of -9 and a y-intercept of 5

f(x)=−9x+5

200

what is the slope and y-intercept of the following function?

y=-x/2+6

slope= -1/2

y-intercpet=6

300

Find an equation for the linear function, "f", if

f(0.4)=–5.9 and f(0.1)=11.5

f(x)=−58x+17.3

400

is the following a linear function?

y=(x+4/x+5) + (x-5/x²-25)

yes, because y=1

500

A company sells chocolate. They incur a fixed cost of $55,000 for rent, insurance, etc. It costs $0.25 to produce each doughnut.

a) Write a linear model to represent the company's cost as a function of the number of doughnuts produced.

b) Find and interpret the y-intercept.

a. C(x)=0.25x+55,000

b) The y-intercept is (0,55,000). If the company does not produce a single doughnut, they still incur a cost of $55,000.

Quadratic Functions

100

what is the y-intercept of the following function?

f(x)=x²+14x-14

y= -14

(0,-14)

200

when does this function reach its minimum?

f(x)=x²-6x+17

(3,8)

300

solve the equation using the quadratic formula:

2x²+5x-3=0

x=1/2

x=-3

400

solve the equation by factoring:

6x²+24x=126

x=-7

x=3

500

The path of an airplane is given the following function, where "h" is the height in yards and "t" is the time in seconds. 

h(t)=—3t2+30t+73

a) At what time does the airplane reach its maximum height? 

b) What is the maximum height of the airplane? 

c) When does the airplane hit the landing (rounded to the nearest second)?

a) 5 secs

b) 148 yds

c) 12 secs