Transformations (2)

Question

When is g(x) = 0 for the function g(x) = 5⋅2^3x + 4?

when x = 0

when x = 1

when x = 4

never

Answer 1

Hi Kyndal R.

For

g(x) = 5 -2^3x + 4

g(x) = -2^3x + 9

When g(x) = 0 you have

0 = -2^3x + 9

Add 2^3x to both sides of your equation

2^3x = 9

Now can you use Change of Base and Logarithms to find x

I got 1.056641667 = x when g(x) = 0

I graphed it a Desmos.com where it was rounded to 1.057, the coordinates (1.057, 0)

I hope this helps and please graph your function so you can see the x and y intercepts

Answer 2

For g(x) = 0, 5·2^3x must equal -4. Since 5 is positive and 2 is positive, no value of x will produce a negative value for the set of real numbers.