Question

1. is the following function linear or nonlinear? how do you know?
2. in the above function, what is the approximate value of y when x = -3?
3. in the above function, what are the approximate values of x when y = 1?
4. could the above function be represented by the equation: y = mx + b? why or why not?

Explanation:

Step1: Analyze linear function criteria

Linear functions form straight lines, with a constant slope and no curvature. The given graph is a curved (parabolic-like) line, so it is nonlinear.

Step2: Locate x=-3 on the graph

Find $x=-3$ on the horizontal axis, then move vertically to the graph. The corresponding $y$-value is approximately 4.

Step3: Locate y=1 on the graph

Find $y=1$ on the vertical axis, then move horizontally to the graph. The corresponding $x$-values are approximately $x=-1$ and $x=-7$.

Step4: Compare to $y=mx+b$ form

The equation $y=mx+b$ defines a linear (straight) function. The given graph is curved, so it cannot fit this form.

Answer:

1. Nonlinear; the graph is a curved line (not straight).
2. $y \approx 4$
3. $x \approx -7$ and $x \approx -1$
4. No; $y=mx+b$ represents a straight linear function, but the given graph is a curved nonlinear function, so it cannot be represented by this equation.