## College Algebra (10th Edition)

(a) Slope $= 0$ and y-intercept $=4$ (b) See the image. (c) Average rate of change $= 0$ (d) The linear function $F(x)=4$ is constant.
Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $F(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$F(x)=4$$ to $$F(x) = mx+b$$ we understand that the slope of the given function is $0$ and its y-intercept is $4$. Note that $F(x)$ can be rewritten as $F(x) = 0\times x + 4$. Step-2: Let us put values of $x$ from $-2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus, For $x=-2$, $F(x)=4$ For $x=-1$, $F(x)=4$ For $x=0$, $F(x)=4$ For $x=1$, $F(x)=4$ For $x=2$, $F(x) = 4$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{F(x_2)-F(x_1)}{x_2-x_1}$$ Let us calculate average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{(4-4)}{2-(-2)}=0$$ Step-4: Since slope, $m=0$, this linear function is constant.