a The x- and y-intercepts are points where the graph crosses the x- and y-axis, respectively.
B
b The x- and y-intercepts are points where the graph crosses the x- and y-axis, respectively.
C
c Start from finding zeros in the table.
D
d You will need to substitute 0 and solve, twice.
A
ax-intercepts: - 1 and 3 y-intercept: - 3
B
bx-intercept: 2 y-intercept: Does not exist.
C
cx-intercepts: - 3, - 1, and 1 y-intercept: 2
D
dx-intercept: 8 y-intercept: - 20
Practice makes perfect
a The x- and y-intercepts are points where the graph crosses the x- and y-axis, respectively. Let's identify them on the given graph.
Now we can determine the coordinates of these intercepts.
As we can see, the graph crosses the x-axis at the points (- 1, 0) and (3,0). Thus the x-intercepts are - 1 and 3. We can also notice that the graph intercepts the y-axis at the point (0,- 3), so the y-intercept is - 3.
b Let's identify the points where the given function crosses either the x - or the y -axis on the graph.
Now we can determine the coordinates of this point.
As we can see, the graph crosses the x-axis at the point (2, 0). Thus, the x-intercept equals 2. We can also notice that the graph does not cross the y-axis, so there is no y-intercept.
c We will identify the x - and y -intercepts of the given relation one at a time.
x
- 5
- 4
- 3
- 2
- 1
0
1
2
y
8
4
0
- 4
0
2
0
- 4
Finding the x-intercept
Think of the point where the graph of a relation crosses the x-axis. The y-value of that ( x, y) coordinate pair is 0, and the x-value is the x-intercept. To find the x-intercept of the relation, we need to find the points where the y-value is 0.
x
- 5
- 4
- 3
- 2
- 1
0
1
2
y
8
4
0
- 4
0
2
0
- 4
We can see that the x-intercepts are - 3, - 1, and 1.
Finding the y-intercept
Let's use the same concept to find the y-intercept. Consider the point where the graph of the relation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, we need to find the point where the x-value is 0.
x
- 5
- 4
- 3
- 2
- 1
0
1
2
y
8
4
0
- 4
0
2
0
- 4
We can see that the y-intercept is 2.
d To determine the x- and y-intercepts of a line, we need to substitute 0 for one variable, solve, then repeat for the other variable.
Finding the x-intercept
Think of the point where the graph of an equation crosses the x-axis. The y-value of that ( x, y) coordinate pair is 0, and the x-value is the x-intercept. To find the x-intercept of the equation, we should substitute 0 for y and solve for x.
An x-intercept of 8 means that the graph passes through the x-axis at the point ( 8,0).
Finding the y-intercept
Let's use the same concept to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.
