Question

A function is defined as a relation for which each x-value has exactly one corresponding y-value. The graph of a function, f(x) is shown below.
Use the graph of the function, f(x), to complete each statement. Enter numerical answers into the spaces provided.

1.f(0)=_____
2.f(2)=_____
3.For the function,f(x), there are exactly three x-values for which the corresponding y-value is zero. In ascending order,f(x), whenx=_____, ______, and______
4.f(-8)=______
5.f(-6)=_______

Answer 1

If you want to evaluate a function $f$ at a specific point $k$, you'll have to look for $k$ on the x axis, and then look vertically for the point on the graph.

The y coordinate of that point is the corresponding y value.

So, for example, if we want $f(0)$, we start from the origin and go up, until we find the point $(0,1)$ that belongs to the graph. So, we have $f(0)=1$.

Similarly, for $f(2)$, we start from 2 on the x axis and go up until we meet the point $(2, 2)$ on the graph. So, we have $f(2)=2$.

For $f(-8)$, we start from -8 on the x axis and go up until we meet the point $(-8, 3)$ on the graph. So, we have $f(-8)=3$.

For $f(-6)$, we start from -6 on the x axis and go down until we meet the point $(-6, -3)$ on the graph. So, we have $f(-6)=-3$.

The three x-values for which the corresponding y-value is zero are the x-coordinates of the points where the graph crosses the x axis (this means that the y axis is zero). Those three points are $(-7, 0),\ (-2, 0),\ (4, 0)$