Question

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Accepted Answer

Step 1: Determine the domain of the function by looking at the x-values covered by the graph. Since the graph extends from x = -2 to x = 5, the domain is all x such that $$-2 \leq x \leq 5. $$Step 2: Determine the range of the function by looking at the y-values covered by the graph. The graph goes from y = 5 down to y = -2, so the range is all y such that $$-2 \leq y \leq 5. $$Step 3: Find the x-intercept(s) by identifying where the graph crosses the x-axis (where $$y=0). $$Locate the point on the graph where the line crosses the x-axis and note the x-coordinate. Step 4: Find the y-intercept by identifying where the graph crosses the y-axis (where $$x=0). $$Locate the point on the graph where the line crosses the y-axis and note the y-coordinate. Step 5: To find the missing function value $$f(-1)$$, use the two known points on the line, $$(-2,5)$$ and $$(5,-2)$$, to find the slope $$m$$ using the formula $$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}. $$Then use the point-slope form of the line equation to find $$f(-1) by $$substituting $$x = -1.$$

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

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Concetti chiave

Domain of a Function

Range of a Function

Finding Function Values from a Graph