Even/Odd/Neither
Describing Transformations
Function Notation and Equations
100
Here is a graph of the function f(x)=x^3
Is f even, odd, or neither? Explain or show your reasoning.
f(x) is an an odd function.
If you reflect the graph across the x-axis, and then across the y-axis, you end up with the same graph. That means that f(x)=-f(-x), which is the definition of an odd function.
100
Describe the transformation that takes the graph of function f to the graph of function g.
f(x)=x^2 and g(x)=x^2+5
Translate 5 units up.
100
Here are the graphs of y=f(x) and y=f(x-1) for a function f.
Which graph corresponds to each equation? Explain how you know.
Green: f(x)
Blue: f(x-1)
The blue graph f(x-1) is translated to the right one unit from the original green function f(x).
200
Is the function k even, odd, or neither? Explain or show your reasoning.
Neither
The function k does not have y-axis symmetry, or 180 degree rotational symmetry, therefore it is neither even nor odd.
200
Here are graphs of functions f and g. Which sequences of transformations take the graph of f to the graph of g? Select all that apply.
A. reflection over the y-axis, then translation up by 2
B. reflection over the x-axis, then translation up by 2
C. translation up 2, then reflection over the y-axis
D. translation up 2, then reflection over the x-axis
E. translation up 2, and then translation left by 5
A. reflection over the y-axis, then translation up by 2
C. translation up 2, then reflection over the y-axis
200
Here are the graphs of two functions, h(t) and k(t), which is a transformation of h(t). Write an equation for the function k(t) in terms of h(t), using function notation.
k(t)=h(t-5)
300
Is f(x) even, odd, or neither? Explain or show your reasoning.
f(x)=x^3-4x
f(x) is an odd function.
f(x)=x^3-4x
f(-x)=(-x)^3-4(-x)
f(-x)=-x^3+4x
f(-x)=-(x^3-4x)
f(x)=-f(-x)
300
Describe how to transform the graph so that it better matches the data.
Option 1: Reflect across the x-axis, and then translate approximately 3 units up.
Option 2: Reflect over the y-axis, then translate about 2 units down and about 3 units to the right.
300
Here are the graphs of the functions f(x) and g(x), which is a transformation of f(x). Write an equation for g(x) in terms of f(x).
g(x)=f(-x)
g(x) is f(x) reflected over the y-axis. Therefore, all the x's need to change sign.
400
Is f(x) even, odd, or neither? Explain or show your reasoning.
f(x)=1/(x^2+1)
Even
f(x)=1/(x^2+1)
f(-x)=1/((-x)^2+1)
f(-x)=1/(x^2+1)
f(-x) is the same as f(x), so the function is even.
400
Describe the transformation that takes the graph of function f to the graph of function g.
f(x)=x^3 and g(x)=-(x-1)^3-5
Reflect over the x, translate 1 unit to the right and 5 units down.
400
Steph Curry shoots a 3 pointer. The basketball's height h, in feet, t seconds after he shoots is modeled by the equation h=9+20t-18t^2 . Which equation models the height of the basketball following the same path but shot 4 seconds earlier?
A) h=5+20t-18t^2
B) h=20t-18t^2
C) h=9+20(t+4)-18(t+4)^2
D) h=9+20(t-4)-18(t-4)^2
C) h=9+20(t+4)-18(t+4)^2
The ball was shot 4 seconds earlier, so we need to translate the function 4 units to the left.
500
Is f(x) even, odd, or neither? Explain or show your reasoning.
f(x)=3^x+3^-x
f(x) is an even function.
f(x)=3^x+3^-x
f(-x)=3^(-x)+3^-(-x)
f(-x)=3^-x+3^x
f(x)=f(-x)
f(-x) is the same as f(x), so the function is even.
500
Describe the transformation that takes the graph of function f to the graph of function g.
g(x)=-f(-x)-3.2
Reflect over the x-axis and y-axis and translate 3.2 units down.
500
Write an equation for g(x) in terms of f(x), if g(x) is f(x) reflected across the x-axis, translated 4 units to the right, and 5 units up.
g(x)=-f(x-4)+5