Math Analysis

Exponential and Log Functions

NOTES: Graphing Exponential Functions y = bx

PART I: Complete each table and then graph. (You do not have to use all the points to graph but will want them to answer the questions that follow.)

A. y = 2x

B. y = 3x

QUESTIONS:

  1. Is the function increasing or decreasing? ______
  2. What is the y-intercept? ______Is this dependent on the value of the base? Why or why not? ______
  3. Will the value of y ever be zero? Why or why not? ______

______

  1. What happens to the value of y as x gets very large? ______
  2. What happens to the value of y as x gets very small? ______
  3. Is there a horizontal asymptote? If so, what is it? ______
  4. Is there a vertical asymptote? If so, what is it?______
  5. What is the domain (the possible values of x)? ______
  6. What is the range (the possible values of y)? ______
  7. Will any of the answer above change if the base changes? If so, how? ______

______

PART II: Complete each table and then graph. (You do not have to use all the points to graph but will want them to answer the questions that follow.)

  1. y = x

B. y = x

QUESTIONS:

  1. Is the function increasing or decreasing? ______
  2. What is the y-intercept? ______Is this dependent on the value of the base? Why or why not? ______
  3. Will the value of y ever be zero? Why or why not? ______

______

  1. What happens to the value of y as x gets very large? ______
  2. What happens to the value of y as x gets very small? ______
  3. Is there a horizontal asymptote? If so, what is it? ______
  4. Is there a vertical asymptote? If so, what is it? ______
  5. What is the domain (the possible values of x)? ______
  6. What is the range (the possible values of y)? ______
  7. Will any of the answer above change if the base changes? If so, how? ______

______

  1. What was the effect of making the base larger? ______

Explain the similarities and difference between the exponential functions when the base, b, is greater than one and the base is between zero and one (a fraction).

PART II: Graph each function and then answer questions.

  1. On the graph is the parent function of y = 2x. Using this same set of axes, graph the function

y = 2x + 3.

QUESTIONS:

  1. What is the effect of adding 3? ______
  2. What do you predict the effect of subtracting 3 would be? ______
  3. Given the general form, y = bx + c, write a general statement of the effect of “c” on the graph of y = bx? ______

B.On the graph is the parent function of y = 3x. Using this same set of axes, graph the function

y = 3x–4.

QUESTIONS:

  1. What is the effect of subtracting 4? ______
  2. What do you predict the effect of adding 4 would be? ______
  3. Given the general form, y = bx + c, write a general statement of the effect of “c” on the graph of y = bx? ______

Without making a table of values, graph the following based on you conclusions above.

  1. y = 4x – 1 + 2
  1. y = 5x + 2 – 4

PART III: Graph each function and then answer questions.

  1. On the graph is the parent function of y = 2x. Using this same set of axes, graph the function

y = 5(2x).

QUESTIONS:

  1. What is the effect of multiplying by 5? ______
  2. What do you predict the effect of multiplying by 1/5 would be? ______
  3. Given the general form, y =abx, write a general statement of the effect of “a” on the graph of y = bxBe sure include when a > 1 and 0 < a < 1? ______

______

B. On the graph is the parent function of y = 2x. Using this same set of axes, graph the function

y = –5(2x).

QUESTIONS:

  1. What is the effect of multiplying by –5? ______
  2. Given the general form, y =abx, write a general statement of the effect of “a” on the graph of y = bx? ______