A dividing function f(x) can be of the form:
[tex]f(x)=\frac{g\mleft(x\mright)}{h(x)}[/tex]
An x-intercept is where the function crosses the x-axis when plotted on a graph.
A y-intercept is where the function crosses the y-axis when plotted on a graph.
Therefore we can construct a dividing function that does cross the x-axis but not the y-axis.
This can be done by adding a constant to the function f(x) so as to shift it up or down, thereby crossing the x-axis
Let us take the function:
[tex]f(x)=\frac{1}{x}[/tex]
as example.
This is plotted below:
As we can see, this graph does not cross either the x or y-axis.
But in order to make it cross the x-axis and hence have an x-intercept, we simply need to add a constant to the function.
We do this by:
[tex]f(x)=\frac{1}{x}+4[/tex]
Plotting this new function, we have:
As we can see, because the graph has been shifted by the constant 4, the graph moves upwards, thereby making it cross the x-axis.
Therefore, the answer is True
