Functions: Basics
What is a function in math?
A rule that gives each input exactly one output.
For y = x + 4, find y when x = 2.
What is 6?
In y = 3x + 2, what is the slope?
What 3?
A line rises from left to right. Is its slope positive or negative?
A line rises from left to right. Is its slope positive or negative?
In y = 2x + 5, what is the y-intercept?
What is 5, or (0,5)?
In f(x) = 2x + 3, what is f(2)?
What is 7
A table has (x,y) = (0,1), (1,3), (2,5). What is the rule?
y = 2x + 1
What is the slope of a horizontal line?
What is 0?
A line drops 3 units for every 1 unit right. What is its slope?
What is -3?
At what x-value does a line cross the y-axis?
What is x = 0 ?
Does the set {(1,2), (2,4), (3,6)} represent a function?
Yes; each input has one output.
For f(x) = -x + 5, what is f(-2)?
What is 7?
Find the slope through (0,1) and (2,5).
What is 2?
A line rises 2 units for every 5 units right. What is its slope?
What is 2/5?
What is the y-intercept of y = -3x - 4?
What is -4, or (0,-4) ?
Does the set {(1,3), (1,5), (2,7)} represent a function? Explain.
No; input 1 has two different outputs.
A function table has x = -1, 0, 1 and y = 2, 4, 6. What is the rule?
y = 2x + 4
Find the slope through (1,6) and (3,2).
What is -2 ?
A line passes through (4,1) and (4,6). What is its slope?
Undefined
Find the y-intercept of a line passing through (0,7) and (2,11).
What is 7, or (0,7) ?
If f(x) = 3x - 2 and f(x) = 10, what is x?
What is 4 ?
A taxi charges $4 plus $2 per mile. Write a function C(m) for m miles.
C(m) = 2m + 4
Find the slope through (-2,-1) and (2,7).
What is 2?
Water fills a tank from 10 gallons to 22 gallons in 4 minutes. What is the rate of change?
3 gallons per minute
A gym charges a $15 sign-up fee and $8 per visit. What does the y-intercept represent?
The $15 sign-up fee (initial cost).