Question

7. The graph of f(x)=−12(14)x−2+4

is shifted downward 4
units, and then shifted left 2
units, stretched vertically by a factor of 4,
and reflected about the x-axis. What is the equation of the new function, g(x)?
State its y-intercept, domain, and range.

Answer 1

Answer: The transformation of the original function f(x) to the new function g(x) can be summarized as follows:

- Shift downward 4 units: f(x) - 4

- Shift left 2 units: f(x + 2) - 4

- Stretch vertically by a factor of 4: 4(f(x + 2) - 4)

- Reflect about the x-axis: -4(f(x + 2) - 4)

Therefore, the equation of the new function g(x) is:

g(x) = -4(1/4)(14)^(x+2) - 4 = -14^(x+2) - 4

The y-intercept of g(x) can be found by setting x = 0:

g(0) = -14^(0+2) - 4 = -200

So the y-intercept of g(x) is -200.

The domain of g(x) is all real numbers since there are no restrictions on the input x.

The range of g(x) is (-∞, -4], which means that the output values of g(x) are always less than or equal to -4.

Explanation: