Functions
f(x)=-4x-10
What is f(3)?
-22
To solve a system of 3 variables, how many distinct equations do you need?
3
y=3x+6
y+2x=-9
(-3, -3)
What is an inverse?
Sample responses: It's when the input and output are exchanged.
A function that maps the output back to the input.
The 'opposite' of a function.
Evaluate
log5125
3
f(x)=(8-x)2
What is f(11)?
Solve by substitution. Express your answer as "x=_ y = _"
x=5
y=x+11
x=5
y=16
What does the graph of a LOGARITHMIC function look like?
Sample answer: It starts at the y-axis at negative infinity, and increases indefinitely by increments of less and less.
How do you find the inverse?
(Write the function in terms of y), switch x and y, and solve for y.
Evaluate. Round to the nearest hundredth.
log8175
2.48
What is the standard form for the polynomial function:
f(x)=8x2 - 5x3 + 2 - 10x?
f(x) = -5x3 + 8x2 - 10x + 2
To solve a system by graphing, you graph both equations. How do you find the solution?
The solution is where the two lines cross.
How do the graph of a function and its inverse relate?
The graph of the inverse is a reflection of the function (over the line y=x).
What is the inverse of
f(x)=x+9
f-1(x)=x-9
log25000
4.40
A small business has 15 customers. The owner sets a goal to grow her business by 20% per year. How many customers will she have in 5 years? (Round to the nearest whole number)
37 customers
Solve by substitution.
2x-5=y-13
y = 10x
x=1,y=10
Is there a solution to the system of equations:
y = 9x - 4
18x-2y = 0
Why or why not?
Sample response:
No, because the lines are parallel and never intersect, therefore there is no solution.
What is the inverse of
f(x)=2x - 18
f-1(x) = x/2 + 9
or
f-1(x) = (x+18)/2
Solve the logarithmic equation:
log (x+3)= log24
x=21
Does the function f(x) = x4 have an inverse (that is a function)? Why or why not?
Sample response: No, f(x) = x4 does not pass the horizontal line test, therefore its inverse does not pass the vertical line test, therefore its inverse is not a function.
What are the two numbers?
18 and 26
A car depreciates in value 16% per year. Gus bought the car in 2020 for $34,000. How much will it be worth in 2045? (Round to dollars and cents)
$434.97
What is f-1(6) according to the table below?
x f(x)
2 8
3 6
4 3
5 0
6 -4
Solve the logarithmic equation:
log6(8x)=3
x=27