Algebra 2 Test Review

Even/ Odd Functions

100

In terms of f(x), what does it mean for a function to be even? What does it mean for a function to be odd? 

Even: f(x) = f(-x)

Odd: -f(x) = f(-x)

200

Is cos(x) even or odd? Must state reasoning

Even. 

Consider: cos(-pi) = -1

cos(pi) = -1

So, cos(-pi) = cos(pi) = -1

300

Is this graph even, odd, or neither? Must state reasoning. 

Neither

400

Is sqrt(x⁴-x²) + 4 even, odd, or neither? (Can write on board)

Even

500

Is f(x) = 1/(x⁵+x-4)+ x² even, odd, or neither? (Can write on board)

Neither

More Even/Odd Functions

100

What are even functions symmetric against? What are odd functions symmetric against? 

Even functions are symmetric against Y-axis. Odd functions are symmetric against origin. 

200

Is sin(x) even, odd, or neither. Must state reasoning. 

Odd

300

Is 4^x+4^-x even, odd, or neither? 

Even

400

Is this graph even, odd, or neither? Must state reasoning. 

Odd. Reflective across origin

500

Is f(x) = sin(x) + 4x³ - (1/x) even, odd, neither? 

Odd

Transformation of functions

100

What transformations take place to y = k(x) for y = 2k(x) + 3? 

- Vertical Stretch by 2

- Vertical Shift by 3

200

What is the name of the transformation that is applied for y = f(x) when it becomes y= f(x+C) for some C that is a constant? 

Horizontal Shift

300

What is the equation for f(x)= -200(1.09)^x translated to the left 5 units and up 20 points? 

f(x) = -200(1.09)^x+5+20 

400

Describe the transformations that take place here: 

- Horizontal Shift to the left 1

-Reflection about x-axis 

-Vertical shift by 2

500

For f(x) = sqrt(x) what is the new function when it is compressed vertically by a factor of 3, reflected across x-axis, translated right 2 units, and translated down 3 units. 

g(x) = -(1/3)sqrt(x-2) - 3

More Transformations of Functions

100

What transformation do you observe here? 

y = f(x-2)

2 points to the right 

200

What is the name of the transformation when a function y = f(x) becomes y=-f(x)? 

Reflection about x-axis

300

What is the name of the transformation of y = f(x) to y = f(-x)?

Reflection above y-axis

400

Describe the transformations that take place here

Vertical compression by 2

Vertical shift by 3

500

What is the new equation for f(x) = (1/x) when there is a vertical shift by 2024, horizontal shift right 4, and vertical stretch by 77? 

f(x) = (77/(x-4)) + 2024

Spring Trivia

100

What does the spring equinox mean?  

The amount of sunlight is the same as the amount of darkness.

200

What day is the first day of spring? 

March 19, 2024

300

What are the three zodiac signs of spring? 

Aries, Taurus, & Gemini 

400

What flower is associated with spring in Japan? 

Cherry Blossoms

500

The first day of spring is a new year in what culture? 

Persian culture