Question

the graphs of f and g are given in the figure.
(a) state the values of f(0) and g(-2).
f(0) =
g(-2) =
(b) which is larger, f(-1) or g(-1)?
〇 f(-1)
〇 g(-1)
(c) for what values of x is f(x) = g(x)? (enter your answers as a comma - separated list.)
x =
(d) on what interval(s) is f(x) ≤ g(x)? (enter your answer using interval notation.)

(e) state the solution of the equation f(x) = -1. (enter your answers as a comma - separated list.)

Explanation:

Step1: Find f(0) from graph

Locate x=0 on the x-axis, the value of f at this point is 3. So $f(0)=3$.

Step2: Find g(-2) from graph

Locate x=-2 on the x-axis, the value of g at this point is 1. So $g(-2)=1$.

Step3: Compare f(-1) and g(-1)

At x=-1, the graph of f is higher than g: $f(-1)=2$, $g(-1)=1$. So $f(-1)$ is larger.

Step4: Find x where f(x)=g(x)

Identify intersection points of f and g: x=-1 and x=2.

Step5: Find interval where f(x)≤g(x)

Identify where g is above or equal to f: from x=-1 to x=2, inclusive.

Step6: Solve f(x)=-1

Find x-values where f(x) = -1: x=3 (and x=-3 is not on the visible graph, only x=3 is clear from the right side of the graph).

Answer:

(a) $f(0)=3$, $g(-2)=1$
(b) f(-1)
(c) $x=-1, 2$
(d) $[-1, 2]$
(e) $x=3$