Functions
What makes up a function table?
Inputs, outputs, and a function
Is this function linear: f(x) = 3x -24
Yes!
Does a nonlinear function take the form: f(x) = mx + b?
Nope! Linear functions do!
If a graph has a straight line, is it linear or nonlinear?
It is linear!
Freebee!
Free points!
Is this function linear: f(x) = 2(x + 6)?
Yes, f(x) = 2x + 12
Is this function nonlinear: f(x) = x4 + 3x + 2?
Yes it is! Our x4 makes our function nonlinear.
If a graph is not a straight line, is it linear or nonlinear?
It is nonlinear!
If we have an input number of x = 6, and the function f(x) = 2x + 5, what is our output number?
Our output number is 17! f(6) = 2(6) + 5 = 12 + 5 = 17.
The point where a line crosses through the y-axis
Is this function nonlinear: f(x) = ex?
Yes! Our x is being altered or manipulated, so we won't have a constant slope.
Why are graphs important?
It helps us visualize our functions!
What is a real world application of a function?
There are many answers! Vending machines, teachers grading homework, putting gas in a car, etc.
What does it mean to be linear?
It has a constant growth, constant slope
What does it mean to be nonlinear?
The function does not grow at a constant rate.
Look at the function: f(x) = 6x + 2. Does this function have an increasing or decreasing slope?
Increasing slope! Since our slope(m) is positive, the graph will have an increasing slope.
When looking at a function table, when can we tell when something is not a function?(This one is tricky!)
If there are multiple outputs for one input!
What form does a linear function take?
A linear function takes the form: f(x) = mx + b, or a straight line
What does a nonlinear graph look like? (many answers for this question)
It won't be a straight line! Could increase quickly, could change how quickly it's growing, etc.
Look at the function: f(x) = 6x + 2. Will the y-intercept be above or below the x-axis?
It will be above the x-axis since our y-intercept is positive!