Function Notation
What is the kind of variable that is inside the parenthesis in function notation?
the input (or independent) variable
What is the highest point of a function?
the maximum
What is the set of all possible output values of a function?
the range
What is found by dividing the difference in the outputs by the difference in the inputs?
the average rate of change
What is the reverse of a function, where the input becomes the output and the output becomes the input?
an inverse function
What is the function notation way of saying that when the input of function f is 12, the output is 43?
f(12) = 43
What is the lowest point of a function?
the minimum
What is the set of all possible input values of a function?
the domain
What is the average rate of change between the following:
the temperature at 6am was 55 degrees
the temperature at 11am was 78 degrees?
(input: hour, output: temperature)
+ 4.6 degrees per hour
What is the inverse of the function c = w + 3 ?
w = c - 3
What is the function notation way of saying that the output of function P is -4.5 when the input is 7?
P(7) = -4.5
What is the point where a function has an x-value of 0?
the y-intercept (or vertical intercept)
What is the domain of a function whose input variable is number of students in this class?
1st hour - D: [0, 11] whole numbers
2nd hour - D: [0, 14] whole numbers
7th hour - D: [0, 10] whole numbers
What is the average rate of change between the following:
Mark was 60 inches tall in 2018
Mark was 67 inches tall in 2022?
(input: year, output: height)
+ 1.75 inches per year
What is the inverse of the function w = d / 7 ?
d = 7w
What is the function notation way of saying that two inputs of function S, 10 and 38, have the same output?
S(10) = S(38)
What is the point where a function has a y-value of 0?
the x-intercept (or horizontal intercept)
What is the domain of a linear function?
all numbers
What is the average rate of change between the following:
Luca has $987 in his bank account in March
Luca has $453 in his bank account in December?
(input: month, output: $)
- $59.33/month
a decrease of $59.33 per month
(200 points if rate is correct but you forgot that it is decreasing or negative)
What is the inverse of the function y = 65 + 5x ?
x = (y - 65) / 5
OR
x = y / 5 - 13
What is the function notation way of saying that the output of function f when the input is 7 is less than the output of function f when the input is 6?
f(7) < f(6)
True or false: A function can have multiple minimum values.
TRUE.
SUPRISE! (Not a domain and range question)
The owner of a restaurant bought 80 pounds of pasta. Each week, the restaurant uses 10 pounds of pasta.
Function p gives the remaining amount of pasta, in pounds, as a function of the number of weeks, w, since the restaurant bought the pasta.
Use function notation to write a rule that defines function p.
p(w) = 80 - 10w
What is the average rate of change between the following points:
(a, f(a)) and (b, f(b)) ?
(f(b) - f(a)) / (b - a)
What is the inverse of the function P(n) = n / 3 - 1.2 ?
n = 3 (P(n) + 1.2)
OR
n = 3P(n) + 3.6