Graphs Exponential Functions

What is the range of the function y = -6^{x + 3} - 9

• (-∞, ∞)

• (-∞, -9)

• (-9, ∞)

• (∞, -∞)

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Abovee

Which the following graphs represents an exponential decay function?

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Given y=3^x determine the y-intercept 

• (0,1)

• (0,3)

What is the asymptote of this function?

• y=-3

• x=-3

• x=0

• y=0

Answer explanation

The blue line in the picture represents the asymptote. This is the line y=0, since all points on this line have a y-value of 0.

Is this function increasing or decreasing?

• Increasing

• Decreasing

Answer explanation

This function is increasing, because as you move from left to right, the y-value get bigger.

What is the y-intercept of this function?

Answer explanation

The function crosses the y-axis at y=-1.

What is the domain of this function?

Answer explanation

The domain of all exponential functions is negative to positive infinity. This is because you can plug in any x-value and get a y-value from the function. We use the curved brackets when the domain or range has infinity.

What is the range of this function?

Answer explanation

This function has an asymptote at y=-2 and is growing. Thus the bottom most y-value is -2, but we use a curved bracket, because -2 is not included (just infinitely close to -2). The function increases forever, so the upper bound is positive infinity.

Is this function increasing or decreasing?

• Increasing

• Decreasing

Answer explanation

This function is decreasing, because as you move from left to right, the y-values get smaller.