Question

1 select the correct answer from each drop - down menu. consider the graph of the parent exponential function f and transformed function g. to produce g, function f was reflected over the x - axis and function g can be defined as

Explanation:

Step1: Analyze horizontal shift

The graph of $g$ is further left - hand side compared to $f$. For a function $y = f(x)$, a shift to the left by $h$ units gives $y=f(x + h)$. Here, it seems to be shifted 1 unit to the left.

Step2: Analyze vertical shift

The $y$ - intercept of $f$ is around 1 and of $g$ is around 4. After reflection over the $x$ - axis and left - shift, we can observe a vertical shift. Since the $y$ - intercept of $g$ is 3 units higher than the reflected and shifted version of $f$'s $y$ - intercept, it is shifted up 3 units.

Let the parent exponential function be $f(x)=a^x$. After reflection over the $x$ - axis, it becomes $y=-a^x$. After shifting 1 unit to the left, it becomes $y = - a^{x + 1}$. After shifting 3 units up, the function $g(x)=-a^{x + 1}+3$.

Answer:

To produce $g$, function $f$ was reflected over the $x$-axis and shifted to the left 1 unit and shifted up 3 units. Function $g$ can be defined as $g(x)=-a^{x + 1}+3$ (where $a$ is the base of the parent exponential function $f(x)=a^x$)