Question

Compare two functions, f(x) and g(x). f(x) is given by the following equation

and g(x) is shown in the graph below. Which of the following statements below is true?
f [x] = 0.5^x - 3

Both functions have the same y-intercept.


f(x) is an increasing exponential function.


g(x) has a greater y-intercept.


f(x) has a greater y-intercept.

Answer 1

True answers:

f(x) is an increasing exponential function.

f(x) has a greater y-intercept

Explanation:

Option 1:

Both functions have the same y-intercept is FALSE

The y-intercept of f(x) is found by plugging in 0 for x

`f(0) = 5^0 - 3 = 1 - 3 = -2`

The intercepts are different, so option 1 is FALSE.

Option 2:

f(x) is an increasing exponential function is TRUE

the largest term is positive and exponential.

Option 3:

g(x) has a greater y-intercept. is FALSE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3

Option 4:

f(x) has a greater y-intercept is TRUE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3