Unit 6: Functions & Function Notation · AI-F.IF.2, AI-F.IF.4
Algebra I Regents
Notes
Read it in English. f(3) = 11 reads “f of 3 equals 11.” If f models height in inches after t years, f(3) = 11 means at 3 years the height is 11 inches.
Vocabulary
function notation: A way to name a function and its output, written f(x).
Practice (no calculator unless marked)
A movie theater’s popcorn box is a rectangular prism with a base that measures 6 inches by 4 inches and has a height of 8 inches. To create a larger box, both the length and the width will be increased by x inches. The height will remain the same. Which function represents the volume, V(x), of the larger box?
A. V(x) = (6 + x)(4 + x)(8 + x)
B. V(x) = (6 + x)(4 + x)(8)
C. V(x) = (6 + x) + (4 + x) + (8 + x)
D. V(x) = (6 + x) + (4 + x) + (8)
Given g(x) = x³ + 2x² − x, evaluate g(−3).
When babysitting, Nicole charges an hourly rate and an additional charge for gas. She uses the function C(h) = 6h + 5 to determine how much to charge for babysitting. The constant term of this function represents
A. the additional charge for gas
B. the hourly rate Nicole charges
C. the number of hours Nicole babysits
D. the total Nicole earns from babysitting
The rule for a function of x is: multiply the input value by 2, then subtract 6. The data set for the input values of the function, x, is {−1, 1, 3, 5}. Which value is one of the output values, y?
A. −2
B. −1
C. 2
D. 4
A movie theater’s popcorn box is a rectangular prism with a base that measures 6 inches by 4 inches and has a height of 8 inches. To create a larger box, both the length and the width will be increased by x inches. The height will remain the same. Which function represents the volume, V(x), of the larger box?
A. V(x) = (6 + x)(4 + x)(8 + x)
B. V(x) = (6 + x)(4 + x)(8)
C. V(x) = (6 + x) + (4 + x) + (8 + x)
D. V(x) = (6 + x) + (4 + x) + (8)
Given g(x) = x³ + 2x² − x, evaluate g(−3).
When babysitting, Nicole charges an hourly rate and an additional charge for gas. She uses the function C(h) = 6h + 5 to determine how much to charge for babysitting. The constant term of this function represents
A. the additional charge for gas
B. the hourly rate Nicole charges
C. the number of hours Nicole babysits
D. the total Nicole earns from babysitting
The rule for a function of x is: multiply the input value by 2, then subtract 6. The data set for the input values of the function, x, is {−1, 1, 3, 5}. Which value is one of the output values, y?