Exponential and Logarithmic Functions

Match

Match the expressions

• $$a^m\cdot a^n=$$

• $$\left(a^m\right)^n=$$

• $$a^{-m}=$$

• $$a^{\frac{m}{n}}=$$

• $$a^0=$$

• $$a^{\left(m+n\right)}$$

• $$a^{mn}$$

• $$\frac{1}{a^m}$$

• $$\sqrt[n]{a^m}$$

• $$1$$

Match

Match the expressions

• $$\ln\left(xy\right)=$$

• $$\ln\left(\frac{x}{y}\right)=$$

• $$\ln\left(x^y\right)=$$

• $$\ln\left(e^x\right)=$$

• $$\ln\left(x\right)+\ln\left(y\right)$$

• $$\ln\left(x\right)-\ln\left(y\right)$$

• $$y\cdot\ln\left(x\right)$$

• $$x$$

​Exponential Functions

Multiple Select

For the expression below,

Select all that are true

$$y=b^x$$

• b is the base

• x is the power/exponent

• H. Asymptote at

  y=0

• y-intercept at

  (0, 1)

• $$\lim_{x\rightarrow\infty}y\ =0$$

​Logarithmic Functions

Multiple Select

For the expression below,

Select all that are true

$$y=\log_b\left(x\right)$$

• b is the base

• x-intercept at

  x=1

• V. Asymptote at

  x=0

• y-intercept at

  (0, 1)

• $$\lim_{x\rightarrow0^+}y\ =-\infty$$

Transformations

Multiple Choice

Describe the transformation of the function $$f\left(x\right)=\log\ x$$

changed to $$f\left(x\right)\ =\ 3\log\left(x+1\right)\ -\ 5$$

• vertical stretch by a factor of 3 and shift right 1 unit and 5 units down

• vertical stretch by a factor of 3, shift left 1 unit and down 5 units

• vertical compress by a factor of 3 and shift right 1 unit and 5 units down

• vertical compress by a factor of 3 and shift left 1 unit and down 5 units

Multiple Select

Select all the transformations that apply to the graph of $$y\ =\ \log_5\left(x+1\right)+1$$

• Horizontal shift left 1 unit

• Horizontal shift right 1 unit

• Vertical shift up 1 unit

• Vertical shift down 1 unit

Multiple Choice

What is the transformation of the parent exponential graph $$y=2^x$$ ?

• Vertical Translation up 2 units and Horizontal translation right 1 unit

• Vertical Translation down 2 units and Horizontal Translation left 1 unit

• Horizontal Translation left 2 units and Vertical Translation up 1 unit

• Horizontal Translation right 2 units and Vertical Translation down 1 unit

Multiple Select

How has the function $$f\left(x\right)\ =\ -\left(3\right)^x+4$$ been transformed from the parent function  $$f\left(x\right)\ =\ \left(3\right)^x$$ ?

Sellect all that apply.

• Shifted up 4 units

• Shifted down 4 units

• Reflected over the x-axis

• Reflected over the y-axis

Multiple Choice

Given the original exponential function defined by $$y=4^x$$ ,

how would the graph change if the function were:

$$y=2\left(4\right)^{\left(x-3\right)}\ +\ 1\$$

• Vertically stretched by a factor of 2, right 3 units, and up 1 unit

• Vertically compressed by a factor of $$\frac{1}{2}$$ , left 3 units and down 1 unit

• Vertically compressed by a factor of $$\frac{1}{2}$$ , right 3 units, and down 1 unit

• Vertically stretched by a factor of 2, left 3 units, and up 1 unit

​Assignments

*New: DM "Unit 2: Exponentials and Logarithms 1"


-Don't forget all assignments are on time until the AP Test (after the test all is late)
-AP Daily Video 3.8
-3.8-3.9 Notes, Practice Test Prep
-Quizizz: 3.10 Practice