(5.2) Transformations
What is the "Parent Function" of all linear functions?
(You may define it or give the equation/function)
Simplest form of a linear function
y=x or f(x)= x
Which function shows a compression of the parent linear function?
1.) g(x)= f(x)
2.) h(x)= 1/2 f(x)
3.) a(x)= 2f(x)
a(x)= 2f(x)
Which representation will you need "rise over run" to help you find slope?
1.) graph
2.) table
3.) relation
1.) Graph
Name the key/ keys that will bring you to the table view of your function:
1.) "y="
2.) "y=" and then "graph"
3.) "graph"
4.) "2nd" and then "graph"
4.) 2nd and then graph
(sure is useful for the quiz tomorrow!)
FREE POINTS
+100 just cause...
What is another word for "shift" when talking about transformations?
Translation
Which function is a shift of f(x)= x?
1.) g(x)= 4f(x)
2.) h(x)= 1/3f(x)
3.) a(x)= f(x)+ 2
a(x)= f(x)+2
The y-values have "shifted" up by 2
FREE POINTS
+200 Just cause...
How can you enter in a function on your calculator?
1.) "graph"
2.) "2nd" and then "graph"
3.) "y="
4.) "x="
3.) y=
(Thank goodness we can use calculators on our quiz tomorrow!!)
How do you read this:
f-1(x)
f inverse
What type of transformation changes the y-intercept of the parent function?
Translation (shift up or down)
Which scenario describes a shift and compression of f(x)=x?
1.) Negative slope, y-intercept= 2
2.) Slope= 5, y-intercept= -3
3.) Slope= 2/3, y-intercept= 1
2.) Slope= 5, y-intercept= -3
The parent function shifted down by 3 and has a slope of 5 as a result of a compression
Which two functions have the same slope?
A.) f(x)= 4x+9
B.) h= {(4,3),(5,6),(6,9)}
C.) g(x)= 3x-2
B and C
h(x) and g(x) both have a slope of 3
What is the full name of your graphing calculator?
TI-84 Graphing Calculator
g(x) looks like a reflection of f(x) over the y=x line
Name the 3 types of transformations that change the slope of the parent function
Reflection
Stretch/Compress
Which question is not appropriate when figuring out whether or not a transformation on the parent linear function has occurred?
1.) Is the slope more curved?
2.) Does the slope look steeper/ less steep
3.) Has the y-intercept changed?
1.) Is the slope more curved
(We are working with linear functions! It should be a straight line, not a curved one!!)
Which two functions have the same y-intercept?
A.) g= {(0,1),(3,4),(6,5),(8,9)}
B.) h(x)= 5x + 2
C.) f(x)= 3x +1
A and C
g(x) has a point (0,1); that means when x=0, y=1. Therefore, 1 is the y-intercept.
f(x) is in the form mx+b where b is the y-intercept. Therefore, 1 is the y-intercept.
If you were trying to find the slope and y-intercept of 2 points, which key would you press first to get started?
1.) "y="
2.) "stat"
3.) "math"
2.) "stat"
(And that is where you can clear/enter your list and calculate the slope and y-intercept)
What is the inverse of f(x)= 2x?
f-1(x)= 1/2x
What is the slope of the parent function after it has been reflected across the x-axis?
m= -1
The slope of the parent function is 1. When it is reflected, the slope is -1
Which function shows two transformations on the parent linear function f(x)=x
1.) g(x)= 4f(x)
2.) r(x)= -1/5 f(x)
3.) a(x)= f(x) + 1
r(x)= -1/5f(x)
The parent function has been reflected (negative slope) and stretched by a factor of 1/5
What is the x-intercept? (Choose 2)
A.) When the graph of the line hits the y-axis
B.) When the graph of the line hits the x-axis
C.) When x=0
D.) When y=0
B and D
x-intercept = when y=0
y-intercept = when x=0
Which keys help you type in a fraction on your calculator?
1.) "y="
2.) "alpha" and then "y="
3.) "alpha" and then 1
2.) alpha and then y=
"Alpha" helps you activate the functions typed in green on your calculator
What is the inverse of f(x)= 1/2x +1/2?
f-1(x)= 2x-1