Question

the graph shows an exponential function, f(x), and a cubic function, g(x). for which interval is f(x) increasing faster than g(x)? options: -3 ≤ x ≤ -2, 2 ≤ x ≤ 3, 0 ≤ x ≤ 1, -2 ≤ x ≤ -1

Explanation:

Step1: Understand the concept

To determine when \( f(x) \) (exponential) is increasing faster than \( g(x) \) (cubic), we look at the steepness of the graphs. The steeper the graph, the faster the function is increasing.

Step2: Analyze each interval

• For \( -3 \leq x \leq -2 \): \( g(x) \) is likely decreasing (since cubic can have negative slope here) and \( f(x) \) is near constant, so \( f(x) \) not increasing faster.
• For \( 2 \leq x \leq 3 \): Observe the graph, the exponential \( f(x) \) (blue) is steeper than cubic \( g(x) \) (red) here, meaning \( f(x) \) is increasing faster.
• For \( 0 \leq x \leq 1 \): Both are increasing, but \( g(x) \) might be steeper or same, not \( f(x) \) faster.
• For \( -2 \leq x \leq -1 \): \( g(x) \) is increasing from low, \( f(x) \) is near constant, so \( f(x) \) not faster.

Answer:

\( 2 \leq x \leq 3 \)