Question

52 for the function $g(x) = 2(6)^x + 4$, as $x \to \infty$, what is y doing? a y is approaching 4 b y is approaching $\infty$ c y is approaching $-\infty$ d y is approaching 0

Explanation:

Step1: Analyze the exponential term

The function is \( g(x) = 2(6)^x + 4 \). For an exponential function \( a^x \) where \( a>1 \), as \( x \to \infty \), \( a^x \to \infty \). Here, \( a = 6>1 \), so \( 6^x \to \infty \) as \( x \to \infty \).

Step2: Analyze the entire function

Multiply the exponential term by 2: \( 2(6)^x \to \infty \) (since multiplying a term that approaches infinity by a positive constant still approaches infinity). Then add 4: \( 2(6)^x + 4 \to \infty + 4=\infty \) as \( x \to \infty \). So \( y = g(x) \) approaches infinity.

Answer:

B. y is approaching \( \infty \)