Question

A linear function, f, has an x-intercept at (5,0) and a y-intercept at (0,3). Which best describes the shape of the graph of this function? As x approaches positive infinity, f(x) approaches 5. As x approaches positive infinity, f(x) approaches negative infinity. As x approaches positive infinity, f(x) approaches 3. As x approaches positive infinity, f(x) approaches positive infinity.

Answer 1

Answer with explanation:

It is given that, a linear function ,f ,has an x-intercept at (5,0) and a y-intercept at (0,3).

Equation of line in  Intercept form, if it cuts intercept of a' on x axis and intercept of b' on y axis, means if the line  passes through (a,0) and (0,b).

$\frac{x}{a}+\frac{y}{b}=1$

So, equation of linear function will be,

 $\frac{x}{5}+\frac{y}{3}=1$

→→3 x + 5 y= 15

When , x→∞,

→5 y = 15 - 3 × ∞

→5 y= - ∞

$y=\frac{-\infty}{5}\\\\ y= -\infty$

Option B: As x approaches positive infinity, f(x) approaches negative infinity.

Answer 2

As x approaches positive infinity, f(x) approaches negative infinity, since the graph goes down