Graph the following rational functions

See attachment.

Step-by-step explanation:

We want to graph the rational function;

The vertical asymptotes occur at where the denominator is zero.

The horizontal asymptote is y=0, since the degree of the numerator is less than the degree of the denominator.

The y-intercept is

The x-intercept is

With this information we can graph the function as shown in attachment.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.