Key features & transforming exponential functions

What is the domain of y=2^x?

• x>0

• x=all real numbers

• y>0

• y=all real numbers

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

What is the range of y=2^x?

• x>0

• x=all real numbers

• y>0

• y=all real numbers

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.C.7

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

• Horizontal shift left one unit
• Horizontal shift right one unit
• Vertical shift up one unit
• Vertical shift down one unit

Tags

CCSS.HSF-IF.C.7E

What transformations have occurred from  $f\left(x\right)=2^x$   to  $g\left(x\right)=-3\left(2\right)^x-7$  

• Reflection across the y-axis, shrink by a factor of 3, horizontal shift left 7 

• Reflection across the asymptote, horizontal shift right 3, vertical shift down 7 

• Reflection across the asymptote, stretch by a factor of 3, vertical shift down 7 

• Stretch by a factor of 3, vertical shift down 7 

Tags

CCSS.HSF.BF.B.3

Describe the transformation of y = 2^x - 3

• left 3

• down 3

• up 3

• right 3

Describe the transformation of

f(x)=-2(3)^x+4 - 8 ?

• right 4, down 8, stretch by a factor of 2, reflect over x-axis

• left 4, down 8, stretch by a factor of 2, reflect over x-axis

• left 4, up 8, compress by a factor of -2

• right 4, down 8, stretch by a factor of 2, reflect over x-axis

What is the end behavior?

• As x approaches infinity, f(x) approaches infinity.

  As x approaches negative infinity, f(x) approaches infinity

• As x approaches infinity, f(x) approaches 0.

  As x approaches negative infinity, f(x) approaches infinity

• As x approaches infinity, f(x) approaches negative infinity.

  As x approaches negative infinity, f(x) approaches infinity

• As x approaches 0, f(x) approaches infinity.

  As x approaches negative infinity, f(x) approaches infinity

What is the end behavior of the function

•  x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
• x →∞, y→∞ and x→⁻∞, y→2
•  x →∞,y→2 and x→⁻∞, y→∞

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Is the function increasing, decreasing, neither, or both?

• increasing

• decreasing

• neither

• both

An exponential decay function increases, decreases, neither, or both?

• increases

• decreases

• neither

• both