Parent Functions
Translations
Dilations & Reflections
Mixed
Miscellaneous
100
Name the parent function.
f(x)=\sqrt { x+3 } -7
What is Square Root Function?
100
Describe the translation.
f(x)= 2^x - 4
Shift Down 4
100
Name the transformation.
f(x)=2x^2
Stretch vertically by a factor of 2 (narrow).
100
Name the transformations.
f(x)=2sqrt(x)-9
Vertical stretch by a factor of 2 (narrow) and shift down by 9.
100
Solve for x:
x^2 - 7x + 2 = 0
What is
x=(7+√41)/2,(7−√41)/2
200
Name the parent function.
What is Exponential?
200
Describe the translation.
f(x)=(x-2)^2+4
Shift Right 2 and Up 4
200
Name the transformation.
f(x)=1/3|x|
Vertical shrink by a factor of 1/3 (wider).
200
Describe the transformations.
f(x)=-1/4x^2-6
Reflection over the x-axis, vertical shrink by a factor of 1/4 (wider), and shift down by 6.
200
What are the roots of the given graph based on the equation:
f(x)=(x+3)(x−2^2(x+1)^3
What is {-3,-1,2)?
300
Name the parent function.
f(x)=root(3)(x-3) -4
What is Cube Root Function?
300
Describe the translation.
f(x)=(x+2)^2
Shift Left 2
300
Name the transformation.
f(x)=-2|x|
Reflection over the x-axis and vertical stretch by a factor of 2 (narrow).
300
Name the transformations.
f(x)=1/4(x-1)^3-5/2
Vertical shrink by a factor of 1/4 (wider), shift right by 1, and shift down by 5/2
300
What are the x-intercepts of the following graph?
What is .5 and 2?
400
Name the parent function.
f(x)= - abs(x + 4) - 3
What is Absolute Value?
400
Describe the translation.
f(x)=|x-2|+3
Shift Right 2 and Up 3
400
Name the transformation.
f(x)=-2x^2
Reflection over the x-axis and vertical stretch by a factor of 2 (narrow).
400
Name the transformations.
g(x)= 2abs(-x-5)
Reflect over y-axis, vertical stretch by a factor of 2 (narrow) and shift right by 5
400
Describes the end behavior of the graph.
As
x->infty, f(x)->infty
x->-infty, f(x)->-infty
500
Name the parent function.
f(x) = (x−3)^2+4
What is a Quadratic Function?
500
Describe the translation.
g(x)=f(x-4)+7
Shift Right 4 and Up 7
500
Name the transformations.
f(x)=2(-x)^2
Vertical stretch by a factor of 2 (narrow) and reflect over the y-axis.
500
Name the transformations.
f(x)= -.5(-x-7)^2 - 3
Reflect over x-axis, reflect over y-axis, vertical shift of .5 (wider), horizontal shift right 7, and shift down by 3.
500
What are the increasing and decreasing intervals are on this graph?
Increasing:
(1,3)and(4,infty)
Decreasing:
(-infty,1)and(3,4)