Transforming Functions: Key Concepts and Techniques

The video tutorial covers homework packet 5'4, focusing on exponential growth through Tasha's savings plan, where she triples her savings each month. Clifton's plan is similar but includes an additional $8. The tutorial explains graphing these functions and introduces circle equations and transformations. It also covers graphing various functions, including reciprocal and square root functions, and discusses how different values affect graph transformations.

What is the starting value (a) in the exponential growth equation for Tasha's savings plan?

• 8

• 5

• 3

• 10

If Tasha triples her savings every month, what is the rate of growth (b) in her exponential equation?

• 4

• 3

• 5

• 2

How does Clifton's savings plan differ from Tasha's in terms of the equation?

• He starts with a different amount

• He doubles his savings

• He adds a constant value

• He subtracts a constant value

What is the effect of adding 8 to Clifton's savings function?

• Shifts the graph left

• Shifts the graph up

• Shifts the graph right

• Shifts the graph down

In a circle equation, what does the term (x - h)² + (y - k)² = r² represent?

• The asymptote of a hyperbola

• The center and radius of the circle

• The slope and intercept of a line

• The vertex of a parabola

If a circle's radius is tripled, how does the equation change?

• The radius term is tripled

• The radius term is cubed

• The radius term is squared

• The radius term is halved

What transformation does the 'a' value cause in a quadratic function?

• Translation

• Vertical stretch/compression

• Horizontal shift

• Reflection over y-axis

How does the 'h' value affect the graph of a function?

• Reflects it over the x-axis

• Shifts it left or right

• Stretches it vertically

• Shifts it up or down

What is the parent function of a reciprocal function?

• y = √x

• y = x²

• y = 1/x

• y = x³

In a cubic function, what does a negative 'a' value indicate?

• Vertical stretch

• Vertical compression

• Reflection over x-axis

• Horizontal shift