Math CHP 7 Quiz

Question 1

The graph of f(x) = c^x . c > 1. is transformed into g(x) = 5c^-4(x-2)

a)The point A (12, -8) on f(x) becomes the point A’ (____, ____) on g(x)

b) What is the y-intercept for g(x)?

A. 1/25c^2

B. 25/c^2

C. 1/c^2

D. 5/c^2

Answer 1

a) (-7/2, -40)

b) D

Question 2

3. Given the function y = c^x, where 0 < c < 1, and a transformed function
   y = -(c^-x)+k where KER, determine the following on the transformed function:

a) Increasing or decreasing function:

b) Range:

c) The equation of any asymptote:

Answer 2

a) Decreasing

b) (y < k)

c) y = -k

Question 3

4. The graph of the equation
   f(x) = (4c^x) - 3, c > 1, has the same horizontal asymptote as which of the following?

A. y = -f(x) - 6

B. y = -f(x) + 6

C. y = -f(x) + 3

D. y = -f(x) - 3

Answer 3

A

Question 4

6. An exponential function is given by
   f(x) = (ac^b(x - h)) + k, where a < 0,
   b < 0, c > 1, h > 0, k > 0, has a range of (-oo, 5). When y = f(x) is vertically stretched by a factor of 2 about the x-axis, shifted right 4 units and down 3 units, determine the equation of any asymptote and range after the transformation.

Answer 4

Asymptote: y = 7

Range = y < 7

Question 5

7. A new car worth $40 000 loses 15% of its value every 2 years. Write an equation that models the value of the car, V, after time, t, in years.

Answer 5

V = 40 000 (0.85)^t/2

Question 6

8. A culture starts with 18 bacteria and reaches 273 bacteria after 24 hours. Write an equation that models the number of bacteria, B, after time, t, in hours. Determine the tripling time, to the nearest tenth of an hour.

Answer 6

9.7 hours

Question 7

10. How many years does $500 need to be invested din an account that earns 6% per annum compounded semi-annually before it increases in value to #8324? Write an equation and then solve graphically, rounded to the nearest tenth.

Answer 7

47.8 years