Question

The y intercept of the graph is at (0,
) (Fill in the y value of this point on the graph)

The horizontal asymptote is at y=

.

The graph is
for all values of x. (increasing or decreasing)

Answer 1

I don’t have the graph or function, so I can’t fill in the specific numbers. Please either upload the graph image or give the function.

Meanwhile, here are quick steps you can use to find each answer:

1. Y-intercept:
- Evaluate the function at x = 0: y-intercept = f(0).
- Example: if f(x) = (2x+1)/(x+3) then f(0)=1/3 so y-intercept is (0, 1/3).

2. Horizontal asymptote y = ?
- Compare degrees of numerator (n) and denominator (d):
- If n < d → horizontal asymptote y = 0.
- If n = d → horizontal asymptote y = (leading coefficient of numerator)/(leading coefficient of denominator).
- If n > d → no horizontal asymptote (there may be an oblique/slant asymptote).
- Example: f(x) = (3x^2 + ...)/(2x^2 + ...) → y = 3/2.

3. “The graph is ___ for all values of x” (increasing or decreasing):
- If it’s a simple function, check f′(x): if f′(x) > 0 for every real x → increasing for all x; if f′(x) < 0 for every real x → decreasing for all x.
- From a graph: if slope is always positive → increasing; always negative → decreasing.
- Example: f(x)=e^x is increasing for all x; f(x)=−e^x is decreasing for all x.

If you upload the graph or give the function, I’ll fill in the exact y-intercept, the horizontal asymptote, and say whether it’s increasing or decreasing.