Let's break down the graph and solve the questions provided:

1. Domain:

The domain of a function is the set of all possible input values (x-values). In the graph, we can see that the line extends infinitely in both the positive and negative x-directions, so the domain is all real numbers:

• Domain: $(-\infty, \infty)$

2. Range:

The range is the set of all possible output values (y-values). Looking at the graph, the y-values go from $-6$ (the lowest point of the graph) to $2$ (the highest point the graph reaches).

• Range: $[-6, 2]$

3. X-Intercept:

The x-intercept is the point where the graph crosses the x-axis (i.e., where $y = 0$). From the graph, we can see that the line crosses the x-axis at $x = 1$.

• X-Intercept: $x = 1$

4. Y-Intercept:

The y-intercept is the point where the graph crosses the y-axis (i.e., where $x = 0$). From the graph, the y-value at $x = 0$ is $-3$.

• Y-Intercept: $y = -3$

5. Function Values:

• $f(-5)$: From the graph, when $x = -5$, the y-value is $-6$.

• $f(0)$: When $x = 0$, the y-value is $-3$.

• Function Values:

  • $f(-5) = -6$
  • $f(0) = -3$

Would you like more details or have any further questions on these calculations? Here are some related questions:

1. How would you find the slope of the line between two points?
2. Can a function have more than one x-intercept? What would it mean graphically?
3. How does the domain of a linear function generally differ from other types of functions?
4. How can you check the accuracy of the y-intercept calculation using the equation of the line?
5. How is the range of a function affected by transformations like shifting or scaling?

Tip: For linear functions, the domain is often all real numbers unless there are specific constraints, such as division by zero or square roots of negative numbers.