Question

The graph of h(x) is shown. Graph of h of x that begins in quadrant two and decreases rapidly following the vertical line which is 5 units to the left of the y-axis. The curve crosses the x-axis 4 units to the left of the origin and crosses the y-axis one unit below the origin and then continues to decrease to the right in quadrant 4. What are the intercepts and asymptote(s) of h(x)? Explain how to find these using the graph.

Answer 1

Answer:

x-intercept

The point at which the curve crosses the x-axis, so when y = 0.

From inspection of the graph, the curve appears to cross the x-axis when x = -4, so the x-intercept is (-4, 0)

y-intercept

The point at which the curve crosses the y-axis, so when x = 0.

From inspection of the graph, the curve appears to cross the y-axis when y = -1, so the y-intercept is (0, -1)

Asymptote

A line which the curve gets infinitely close to, but never touches.

From inspection of the graph, the curve appears to get infinitely close to but never touches the vertical line at x = -5, so the vertical asymptote is x = -5

(Please note:  we cannot be sure that there is a horizontal asymptote at y = -2 without knowing the equation of the graph, or seeing a larger portion of the graph).

Answer 2

#1

x intercept is the point where h(x) crosses x axis

• (-4,0)

y intercept is the point where h(x) crosses y axis

• (0,-1)

#2

asymptotes are those lines which the function tries to cross but never crosses

Here vertical asymptote is

• x=-5

The horizontal asymptote is

• y=-2