17. what is the domain and range of the exponential function in inequality notation?\n$f(x)=2^{x}-4$\ndomain…

17. what is the domain and range of the exponential function in inequality notation?\n$f(x)=2^{x}-4$\ndomain: $-\\infty < x < \\infty$\nrange: $y > -4$\ndomain: $x > -4$\nrange: $-\\infty < y < \\infty$\ndomain: $-\\infty \\leq x \\leq \\infty$\nrange: $y \\geq -4$\ndomain: $-\\infty < x < \\infty$\nrange: $y < -4$

17. what is the domain and range of the exponential function in inequality notation?\n$f(x)=2^{x}-4$\ndomain: $-\\infty < x < \\infty$\nrange: $y > -4$\ndomain: $x > -4$\nrange: $-\\infty < y < \\infty$\ndomain: $-\\infty \\leq x \\leq \\infty$\nrange: $y \\geq -4$\ndomain: $-\\infty < x < \\infty$\nrange: $y < -4$

Answer

Explanation:

Step1: Find domain of $2^x$

The function $2^x$ accepts all real numbers, so domain is $-\infty < x < \infty$.

Step2: Find range of $2^x$

For all real $x$, $2^x > 0$.

Step3: Adjust range for $f(x)=2^x-4$

Subtract 4 from the inequality: $2^x - 4 > 0 - 4$, so $f(x) > -4$ (or $y > -4$; note: the first option uses $\geq$ which is a minor notation nuance, but it is the only one matching the domain and correct range direction).

Step4: Match to options

The domain is $-\infty < x < \infty$, range is $y > -4$ (the first option's $\geq$ is the closest valid choice as others are incorrect).

Answer:

A. Domain: $-\infty < x < \infty$ Range: $y \geq -4$