Question

3. The graph of a function g is given.

a. Which is larger f(0)or g(0) ?
b. Which is larger f(-3) or g(-3) ?
c.For which values of x is f(x)= g(x)?

Answer 1

Please check the explanation.

Explanation:

Given the graph of a function f and g.

Part a)

From the graph, it is clear that:

at x = 0, the value of y of function f is 3.

i.e. f(0) = 3

and

at x = 0, the value of y of function g is 0.5

i.e. g(0) = 0.5

Conclusion:

f(0) = 3

g(0) = 0.5

Therefore,

• f(0) is larger.

Part b)

From the graph, it is clear that:

at x = -3, the value of y of function f is -1.

i.e. f(-3) = -1

and

at x = -3, the value of y of function g is 2

i.e. g(-3) = 2

Conclusion:

f(-3) = -1

g(-3) = 2

Therefore,

• g(-3) is larger.

Part c)

From the graph, it is clear that at x = 2 and x = -2, both the graphs meet.

From the graph it is clear that:

• at x = 2, f(2) = 2 and g(2) = 2

• at x = -2, f(-2) = 1 and g(-2) = 1

In other words, both graphs are equal at x = 2 and x = -2.

i.e.

f(x) = g(x) at x = 2 and x = -2

Answer 2

Explanation

• Which is larger f(0) or g(0)?

At the specific domain x = 0. Larger means that graph is above another graph.

At x = 0, we can see that function f covers the function g. Therefore, function f is larger.

• Which is larger f(-3) or g(-3)?

This is the same as first question. Look at x = - 3. Notice that the graph of function g is above graph of function f at x = - 3. Therefore function g is larger.

• For which values of x is f(x)=g(x)?

Both graphs have intercepts to each others. Look at both graphs and you will see that f(x)=g(x) when x = -2,2

Answer

`\large \boxed {1. \: f(0)} \\ \large \boxed {2. \: g( - 3)} \\ \large \boxed {3. \: x = -2,2}`