To find the intercepts on a graph of a function, we need to look for two key points: the x-intercept and the y-intercept.
The x-intercept is the point where the graph touches the x-axis. At this point, the output (or y-value) is zero. To find it, we set the equation equal to zero.
Let’s look at an example. For the function ( f(x) = x^2 - 4 ), we want to solve for when it equals zero:
[ x^2 - 4 = 0 ]
When we solve this, we find two values: ( x = 2 ) and ( x = -2 ).
So, the x-intercepts are at the points (2, 0) and (-2, 0).
Next, we find the y-intercept. This is where the graph crosses the y-axis. To do this, we set ( x = 0 ) in the function.
For our function, we calculate:
[ f(0) = 0^2 - 4 = -4 ]
This tells us that the y-intercept is at (0, -4).
Knowing these intercepts helps us understand how the graph looks and behaves!
To find the intercepts on a graph of a function, we need to look for two key points: the x-intercept and the y-intercept.
The x-intercept is the point where the graph touches the x-axis. At this point, the output (or y-value) is zero. To find it, we set the equation equal to zero.
Let’s look at an example. For the function ( f(x) = x^2 - 4 ), we want to solve for when it equals zero:
[ x^2 - 4 = 0 ]
When we solve this, we find two values: ( x = 2 ) and ( x = -2 ).
So, the x-intercepts are at the points (2, 0) and (-2, 0).
Next, we find the y-intercept. This is where the graph crosses the y-axis. To do this, we set ( x = 0 ) in the function.
For our function, we calculate:
[ f(0) = 0^2 - 4 = -4 ]
This tells us that the y-intercept is at (0, -4).
Knowing these intercepts helps us understand how the graph looks and behaves!