Question

H(x) = 2x-6/x+3

Which statements are true or false about the graph of function h?


The graph crosses the y-axis at (0,3).


The graph crosses the x-axis at (-2,0)


The graph has a vertical asymptote at r = -3.


The graph has a hole at (3,0).


The graph has a horizontal asymptote at y = 2


The domain of the function does not include the values x= -3 and x= 3.

Answer 1

Answer:image

Explanation:

Answer 2

The correct option is;

The graph has a vertical asymptote at x = -3

Explanation:

Whereby the given function is
`h(x) = 2\cdot x - (6)/(x + 3)`, we have;

The function is undefined at x = -3, therefore, the function has a verical asymptote at x = -3

The graph crosses the x-axis (the x-intercept) when the y coordinate, value h(x) = 0, therefore, we have;

`2\cdot x - (6)/(x + 3) = 0 \ at \ the \ x-intercept`

Which gives;

`2\cdot x = (6)/(x + 3)`

2·x² + 6·x - 6 = 0

Dividing by 2 gives;

x² + 3·x - 3 = 0

x = (-3 ± √(3² - 4×1×(-3)))/(2 × 1) = (-3 ± √21)/2

Similarly, the y-intercept occurs when h(0) = -2 as follows;

`h(0) = 2* 0 - (6)/(0 + 3) = -2`

Therefore, the graph crosses the y-axis, the y-intercept at (0, -2)

The correct option is, that the graph has a vertical asymptote at x = -3