1-31-2025

Last updated 8 months ago

9 questions

Do Now-

Assume f(x)=x^{2}, describe the transformation of 3f(x)+5.

Periodic

Recall that angles have an infinite amount of co-terminal angles

Creating the graphs

Now you build the graph for cos(x)

Domain and Range

Shifting

Given that f(x)=\sin(x) , what do you think would happen if we graph the following (no desmos)

f(x)=\sin(x)+3
_______ 
f(x)=\sin(x)-7
_______ 
f(x)=\sin(x)+\pi
_______ 

Midline

For both f(x)=\sin(x)+k and f(x)=\cos(x)+k, the midline of the function is y=k.

Identify the midline of each function

f(x)=\sin(x)+3
_______ 
f(x)=\sin(x)-7
_______ 
f(x)=\sin(x)+\pi
_______ 

f(x)=\cos(x)-4
_______ 
f(x)=\cos(x)+15
_______ 
f(x)=\cos(x)+e
_______ 

Amplitude

Given that f(x)=\sin(x) , what do you think would happen if we graph the following (no desmos)

f(x)=3\sin(x)
_______ 
f(x)=7\sin(x)
_______ 
f(x)=\pi\sin(x)
_______ 

Amplitude

For both f(x)=A\sin(x) and f(x)=A\cos(x), the amplitude will be |A|

Identify the amplitude of each function

f(x)=3\sin(x)
_______ 
f(x)=7\sin(x)
_______ 
f(x)=\pi\sin(x)
_______ 

f(x)=4\cos(x)
_______ 
f(x)=15\cos(x)
_______ 
f(x)=e\cos(x)
_______ 

Combining the concepts

Your Practice