Question

1. (1 point) the graph of g is shown below. sketch the graph of g.

Explanation:

Step1: Identify the function type

The function $g(x)$ is a linear - function. The general form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. From the graph, the y - intercept $b = 2$ and using two points $(0,2)$ and $(1,0)$, the slope $m=\frac{0 - 2}{1-0}=- 2$. So $g(x)=-2x + 2$.

Step2: Recall the derivative of a linear function

The derivative of a linear function $y = mx + b$ is given by the formula $\frac{d}{dx}(mx + b)=m$. Since $m=-2$ for $g(x)=-2x + 2$, the derivative $g^{\prime}(x)=-2$.

Step3: Sketch the graph of $g^{\prime}(x)$

The graph of $g^{\prime}(x)=-2$ is a horizontal line at $y = - 2$ for all real values of $x$.

Answer:

The graph of $g^{\prime}(x)$ is a horizontal line at $y=-2$ across all real - valued $x$.