Exponential Functions Unit Part 2

Question 1

What is the “parent” form

Answer 1

p(x) = b^x

Question 2

What does b represent?

Answer 2

B is the base and it’s a constant positive real number other than one

Question 3

What does x represent?

Answer 3

X represents the exponent and it’s the independent variable (the input value of the function)

Question 4

What does a represent?

Answer 4

A represents a constant being multiplied to the parent function

Question 5

What happens if a < 0?

Answer 5

There’s a reflection over the x-axis and the range and y-intercept are effected

Question 6

What happens when the absolute value of a is greater than 1?

Answer 6

Vertical stretch by a factor of “a” (the y-intercept is effected)

Question 7

What happens when the absolute value of a is greater than 0 and less than 1?

Answer 7

Vertical compression by a factor of “a” (the y-intercept is effected)

Question 8

What is the standard form of an exponential function with transformations applied?

Answer 8

n(x) = ab^x - h + k (n(x) could be replaced with Y, etc because it still represents y and b is raised by x - h (and if the value h is negative then h is positive and if the value of h is negative then h is positive because of the negative sign)

Question 9

What does the value of h affect?

Answer 9

1. If h > 0, the graph translates right by the absolute value of h (h determines the horizontal translation)
2. If h < 0 the graph translates left by the absolute value of h
   (h determines the horizontal translation)

(both affect the y-intercept)

Question 10

What does the value of k affect?

Answer 10

1. If k > 0, vertical translation up by the absolute value of k
   (k determines the vertical translation)
2. If k < 0, vertical translation down by the absolute value of k
   (k determines the vertical translation)

(both affect the range, the y-intercept, and the asymptote (y = k))