Questions: Consider the function graphed. The function has a Select an answer of at x= The function is increasing on the interval(s): The function is decreasing on the interval(s):

Consider the function graphed.

The function has a Select an answer of at x=
The function is increasing on the interval(s):
The function is decreasing on the interval(s):

Transcript text: Consider the function graphed. The function has a $\square$ Select an answer of at $x=$ $\square$ The function is increasing on the interval(s): $\square$ The function is decreasing on the interval(s): $\square$

Solution

Solution Steps

Step 1: Determine the minimum value and its corresponding x-value.

The lowest point on the graph is at $y = -1$, which occurs at $x = 2$. This point $(2, -1)$ is the vertex of the parabola.

Step 2: Determine where the function is increasing.

The function is increasing when the y-values increase as the x-values increase. Looking at the graph, this occurs for all $x$-values greater than $2$. So, the interval where the function is increasing is $(2, \infty)$.

Step 3: Determine where the function is decreasing.

The function is decreasing when the y-values decrease as the x-values increase. Looking at the graph, this occurs for all $x$-values less than $2$. So, the interval where the function is decreasing is $(-\infty, 2)$.

Final Answer

The function has a minimum of at $x=2$. The function is increasing on the interval(s): $(2, \infty)$. The function is decreasing on the interval(s): $(-\infty, 2)$.

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