Chapter 1.2, Problem 6E

To determine

To find: The common members of the family of linear function $f\left(x\right)=1+m\left(x+3\right)$; sketch and mark the members on the graph.

Answer to Problem 6E

The members of the family of a linear function $f\left(x\right)=1+m\left(x+3\right)$ pass through the common point (−3, 1).

Explanation of Solution

Consider the linear function $y=1+m\left(x+3\right)$.

Recall the fact that the slope (m) of the function is the coefficient of the x term and y-intercept (c) is the constant term of the function.

Obtain the values of y-intercepts for the various m values.

If $m=1$, then $c=4$.

If $m=-1$, then $c=-2$.

If $m=0$, then $c=1$.

If $m=2$, then $c=7$.

Substitute the above values of m and corresponding values of c in the linear function $y=mx+c$ and draw the graph of them as shown below in Figure 1.

From Figure 1, it is noticed that all the members of the family of a linear function $f\left(x\right)=1+m\left(x+3\right)$ passes through the common point (−3, 1).