Exercise 8 Page 234

We are given a graph with the function g(x) plotted on it. Furthermore, we are told that f(x) has a slope of -3 and a y-intercept of 5. We need to find a rule for each function and compare their domains, ranges, slopes, and y-intercepts. Let's start by recalling the slope-intercept form of a line. y=mx+b In the above formula, m is the slope and b is the y-intercept. We need to find the slope and y-intercept to write each function rule. We will work each case independently to find their rules and characteristics. We will compare them at the end.

Finding a rule, domain and range for g(x)

We can use the graph of g(x) to find its y-intercept and its slope.

From the graph we can see that the function g(x) intersects the y axis at (0,6). Hence, its y-intercept is 6. Furthermore, notice that the function moves down 10 units as it moves 4 units to the right. Therefore its slope is m= -104= - 52. With this in mind, we can now write the function rule for g as follows. g(x)= -5/2x+ 6 Recall that the domain of a function is the set of all possible x-values, while the range is the set of all possible y-values. Since the line extends infinitely, the domain and range of g(x) contains all the real numbers. Domain:& - ∞ < x < ∞ Range:& - ∞ < g(x) < ∞

Finding a rule, domain and range for f(x)

For f(x) the task is easier since we are told that its slope m is -3, and the y-intercept b is 5. Hence, we can write its equation. f(x)= -3x+ 5 Again, since f(x) is a line, it extends infinitely by definition. Thus, its domain and range contain all the real numbers. Domain:& - ∞ < x < ∞ Range:& - ∞ < f(x) < ∞

Comparison chart

The corresponding information for each graph is shown in the table below for easier comparison.