Question

select the correct answer.

consider the graph of the function (f(x) = 10^x).

what is the range of function (g) if (g(x) = -f(x) - 5)?

({y | -infty < y < -5})
({y | -5 < y < 0})
({y | -infty < y < infty})
({y | -5 < y < infty})

Explanation:

Determine the range of the parent function

$$ \text{Range of } f(x) = 10^x \implies (0, \infty) \quad \text{or} \quad \{y \mid 0 < y < \infty\} $$

Apply the transformations to the range

$$
LATEXBLOCK0
$$

State the range of the transformed function

$$ \text{Range of } g(x) \implies \{y \mid -\infty < y < -5\} $$

Answer:

• (A) \(\{y | -\infty < y < -5\}\) (Correct answer)
• (B) \(\{y | -5 < y < 0\}\)
• (C) \(\{y | -\infty < y < \infty\}\)
• (D) \(\{y | -5 < y < \infty\}\)