Graphs of Exponential Functions

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.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.6

CCSS.HSF.IF.C.7

What is the y-intercept of this function?

Answer explanation

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

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSS.ID.C.7

What is the x-intercept of this function?

Answer explanation

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

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

What is the asymptote of this function?

• y=2

• y=-2

• x=-2

• x=3

Answer explanation

The blue line in the picture represents the asymptote. This is the line y=-2, since all points on this line have a y-value of -2.

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

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.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

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.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

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.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the asymptote of this function?

• y=4

• y=-4

• x=2

• x=4

Answer explanation

The blue line in the picture represents the asymptote. This is the line y=4, since all points on this line have a y-value of 4.

Tags

CCSS.HSF.IF.C.7

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. Always list the domain from lowest value to highest value.

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.5

What is the range of this function?

Answer explanation

This function has an asymptote at y=4 and is decreasing. The bottom bound will be negative infinity. The top most y-value is 4, but we use a curved bracket, because 4 is not included (just infinitely close to 4).

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7