Square Root Function
What is a one-to-one function?
For every one input there is one output.
what is the parent formula for Square Root Functions?
f(x) = √x
What is the name of the tiny number in front of the radical?
index
How do you know if a function is a compression?
What is the Greatest Integer Function?
the greatest integer less than or equal to your x-input
When do you use a horizontal line test?
To see if a function is a one-to-one.
When |a| < 1, the graph of g(x) is a vertical ________ of the graph of the parent function.
Compression
what is the difference between a Square Root function and a Cube Root function (when graphing)?
Square root has an end point
Cubed root is endless
How do you know when a graph has a stretch?
when a > 1
What shape is the graph of a piecewise function compared to an Absolute Value Functions?
Piecewise: A straight line
Absolute Value: V shape
How do we find the inverse formula f-1(x)?
Replace f(x) with y and solve for x
When |a| > 1, the graph of g(x) is a vertical _______ of the graph of the parent function.
stretch
What are the domain and ranges for cub root functions once graphed?
All real numbers
what letter dictates if there is a translation?
A
What is the difference between brackets, bars, and parenthesis?
Brackets: Greatest Integer Function
Bars: Absolute Value
Parenthesis: grouping
When finding the domain of square root functions, what part of the the equation are you solving for?
you solve only what is under the radical
how do different values of a in the function
f(x) = a √ x − h + k will affect the range.
it will determine if you have a stretch or compression.
When given a radical in your formula, what numbers do you use for your x-inputs?
-8, -1, 0, 1, 8
What pattern do we see when we create out input and output (x,y) chart?
it reflects positive and negative numbers
What is the General Form Formula for Absolute Value functions?
f(x) = a|x – h| + k
Why is a linear function not one to one if the slope is 0?
It would be a horizontal line and there will be the multiple same y-values. It will fail the horizontal line test.
State the steps to write an equation for a Square Root function.
know the formula
identify your end point (h,k)
plug in for f(x) and x variable
solve for a
When writing your inverse rule for Cubed functions, what must your radical include?
3 as your index
Can a one cube root function have a compressional stretch with a translation?
NO!
It's either a Compression or a stretch. Compressional stretch is not a thing.
When solving absolute value inequalities, what does your graph look like? Include all characteristics (4)
A number line, with two cases, open or closed circles, and shading.