Question

1. use these key features to sketch the graph of f(x): ● linear ● increasing for no values of x ● y - intercept located at (0, 3) ● x - intercept located at (2, 0) ● end behavior: as x→∞, y→ - ∞

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $y$-intercept $(0,3)$, so $b = 3$.

Step2: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the $y$-intercept $(0,3)$ and $x$-intercept $(2,0)$, we have $m=\frac{0 - 3}{2-0}=-\frac{3}{2}$.

Step3: Sketch the line

Plot the $y$-intercept $(0,3)$ and the $x$-intercept $(2,0)$. Since the line is linear with slope $m =-\frac{3}{2}$ and as $x\to\infty,y\to-\infty$, draw a straight line passing through these two points.

Answer:

Sketch a straight line passing through the points $(0,3)$ and $(2,0)$.