Understanding Graphs and Functions

The video tutorial guides students through matching graphs with function definitions. It explores the behavior of functions at x=0, as x increases, and as x decreases. The tutorial provides detailed analysis of specific functions, including y=1/2^x-2, y=2^x, and y=-3^x, helping students understand their graphical representations and behavior.

What is the initial value of y when x is 0 for the function y = 2 - 1/3^x?

• 1

• 0

• -1

• 2

As x becomes very large, what value does y approach in the function y = 2 - 1/3^x?

• 1

• 0

• -1

• 2

For the function y = 1/2^x - 2, what is the value of y when x is 0?

• 0

• 1

• -1

• -2

As x increases, what value does y approach in the function y = 1/2^x - 2?

• -2

• -1

• 1

• 0

What is the initial value of y when x is 0 for the function y = 2^x?

• -1

• 2

• 1

• 0

What happens to y as x becomes more negative in the function y = 2^x?

• y approaches 0

• y approaches 1

• y approaches 2

• y becomes negative

Which function is represented by a classic exponential graph shape?

• y = -3^x

• y = 2 - 1/3^x

• y = 2^x

• y = 1/2^x - 2

In the function y = -3^x, what is the value of y when x is 0?

• -1

• 1

• -3

• 0

What is the effect of the negative sign in the function y = -3^x?

• It shifts the graph down

• It reflects the graph over the y-axis

• It shifts the graph up

• It reflects the graph over the x-axis

As x becomes more negative in the function y = -3^x, what does y approach?

• 0

• 1

• -1

• -3