Question

what is the equation of the parent function?
$f(x)=2^x$
$f(x)=x^3$
$f(x)=x$
$f(x)=|x|$

Explanation:

Step1: Identify curve type

The graph shows a decreasing exponential curve, which matches the shape of $f(x)=b^x$ where $0

Step2: Match to parent function

The given option $f(x)=2^x$ is the parent exponential function; the graph is a transformation (reflection, shift) of this parent function, while the other options have distinct graph shapes: $f(x)=x^3$ is cubic, $f(x)=x$ is linear, $f(x)=|x|$ is absolute value.

Answer:

$f(x)=2^x$