Module 1 Transformations

Question 1

What is the vertex form formula?

Answer 1

y= a(x - h)2 + k

Question 2

What do each of the letters represent in the vertex for and why?

Answer 2

a = vertical stretch because it is outside the brackets effecting the “y” value and is multiplied

h = horizontal shift because it is inside the brackets effecting the “x” value and is added

k = vertical shift because it is outside the brackets effecting the “x” value and is added

Question 3

How do we know when the value is a shift or a stretch?

Answer 3

Shift - add or subtract

Stretch - multiply or divide

Question 4

What are the types of reflections and describe what happens

Answer 4

Vertical reflection - the negative affects the “y” value

Horizontal reflection - the negative affects the “x” value

Reflection about the line y=x - x becomes y and y becomes x

Question 5

What is the point form and formula form for each reflection?

Answer 5

Vertical reflection
(x,y) —> (x,-y)
y=f(x) —> y=-f(x)

Horizontal reflection
(x,y) —> (-x,y)
y=f(x) —> y=f(-x)

Reflection about line y=x
(x,y) —> (y,x)
y=f(x) —> y=f-1(x)

Question 6

What are the steps to convert an absolute value function to piece-wise function?

Answer 6

1) split absolute in to two equations (positive and negative) and simplify
2) find restrictions by only taking the absolute into an equation that equals 0
3) write in piece-wise form

Question 7

Do we finish the piece-wise function with }? Why?

Answer 7

No, because there is not one solution

Question 8

What are the steps to graphing absolute value function?

Answer 8

1) graph inside absolute

2) keep the graph above the x-axis

Question 9

What are the horizontal asymptotes?

Answer 9

Top degree is larger than bottom degree HA: N/A

Top degree is smaller than bottom degree HA: y=0

Degrees are the same HA: y= top leading coefficient / bottom leading coefficient

Question 10

What is the point form and formula form for reciprocals?

Answer 10

y= 1/f(x)

x,y) —> (x,1/y

Question 11

What are the steps to graphing reciprocal functions?

Answer 11

1) graph the denominator (original function)
2) find horizontal asymptote
3) find vertical asymptotes (from step one or where x cannot =0
4) Use reciprocal method for the rest of the points on the graph (x,1/y) START WITH POINTS (±1, ±1)
5) preform transformation