Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 17, 2024

Shift $f(x)=6^{x}$ to get $g(x)=6^{x-5}-7$ . Which steps work?

STEP 1

Assumptions
1. The original function is $f(x) = 6^{x}$ .
2. The transformed function is $g(x) = 6^{x-5} - 7$ .
3. A horizontal shift to the right is indicated by a subtraction inside the function argument (to the $x$ value).
4. A horizontal shift to the left is indicated by an addition inside the function argument (to the $x$ value).
5. A vertical shift upwards is indicated by an addition outside the function.
6. A vertical shift downwards is indicated by a subtraction outside the function.

STEP 2

Identify the horizontal shift by examining the argument of the function.
The function $g(x)$ has $x-5$ in the exponent, which means the function $f(x)$ is shifted horizontally.

STEP 3

Determine the direction and magnitude of the horizontal shift.
Since $g(x)$ has $x-5$ in the exponent, this indicates a shift to the right by 5 units.

STEP 4

Identify the vertical shift by examining the constant term outside the function.
The function $g(x)$ has $-7$ outside the exponentiation, which means the function $f(x)$ is shifted vertically.

STEP 5

Determine the direction and magnitude of the vertical shift.
Since $g(x)$ has $-7$ outside the exponentiation, this indicates a shift downwards by 7 units.

STEP 6

Combine the horizontal and vertical shifts to describe the transformation from $f(x)$ to $g(x)$ .
The function $f(x) = 6^{x}$ is shifted five units to the right and seven units down to obtain $g(x) = 6^{x-5} - 7$ .
The correct set of steps to translate $f(x) = 6^{x}$ to $g(x) = 6^{x-5} - 7$ is: Shift $f(x) = 6^{x}$ five units to the right and seven units down.

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms