Question

matq 1099
midterm 1
page 4 of 6

1. use the graph of the function f(x) to find

(2 marks)
a) the x-value(s) for which f(x) = -2.
b) f(-6).

1. a. ________

b. ________

1. solve and graph the solution: $-5\leq 4-3x\leq 2$

(2 marks)

1. ________

Explanation:

For Question 11:

a) Locate $y=-2$ on the graph, find the corresponding $x$-values where the function intersects this horizontal line.
b) Locate $x=-6$ on the graph, find the $y$-value of the function at this point.

Step1: Isolate the variable term

Subtract 4 from all parts:
$-5 - 4 \leq 4 - 3x - 4 \leq 2 - 4$
$\implies -9 \leq -3x \leq -2$

Step2: Reverse inequalities when dividing by negative number

Divide all parts by $-3$:
$\frac{-9}{-3} \geq \frac{-3x}{-3} \geq \frac{-2}{-3}$
$\implies 3 \geq x \geq \frac{2}{3}$

Step3: Rewrite in standard order

$\frac{2}{3} \leq x \leq 3$

Step4: Graph description

On a number line, plot closed circles at $x=\frac{2}{3}$ and $x=3$, then shade the region between the two points.

Answer:

a) $x = -4$ and $x = 2$
b) $f(-6) = 4$

---

For Question 12: