Question

Which statement is true regarding the graphed functions?

f(0) = 2 and g(–2) = 0
f(0) = 4 and g(–2) = 4
f(2) = 0 and g(–2) = 0
f(–2) = 0 and g(–2) = 0

Answer 1

let's analyze each case to determine the solution

case 1) f(0) = 2 and g(–2) = 0

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 1) is false

case 2) f(0) = 4 and g(–2) = 4

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 2) is false

case 3) f(2) = 0 and g(–2) = 0

For x=2-----> find the value of f(2) in the graph-----> f(2)=0

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 3) is true

case 4) f(–2) = 0 and g(–2) = 0

For x=-2-----> find the value of f(-2) in the graph-----> f(-2) is greater than 12

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 4) is false

therefore

the answer is

f(2) = 0 and g(–2) = 0-------> this statement is true

Answer 2

The correct option is $\boxed{\left(c\right)f\left(2\right)=0{\text{ and }}g\left({-2}\right)=0}$.

Further explanation:

Consider a function $f\left(x\right)$ as $y$.

$\boxed{f\left(x\right)=y}$                                                     ...... (1)

Consider the function $g\left(x\right)$ as $z$.

$\boxed{g\left(x\right)=z}$                                                   ...... (2)

Substitute 0 for $x$ in equation (1) to obtain the value of $f\left(0\right)$ and also the value of $f\left(0\right)$ can be obtained from the graph by finding the value of $y$ at $x=0$.

$\boxed{f\left(0\right)=4}$

Substitute 2 for $x$ in equation (1) to obtain the value of $f\left(2\right)$ and also the value of $f(2)$ can be obtained from the graph by finding the value of $y$ at $x=2$.

$\boxed{f\left(2\right)=0}$

Substitute $-2$ for $x$ in equation (2) to obtain the value of $g(-2)$ and also, the value of $g(-2)$ can be obtained from the graph by finding the value of $z$ at $x=-2$.

$\boxed{g\left({-2}\right)=0}$

Now check the option that is satisfied by the obtained value.

In the option (a) the value of $f(0)$ is 2 which is not equal to the obtained value so this option is not correct.

In the option (b) the value of $f(0)$ is 4 which is not equal to the obtained value so this option is not correct.

In the option (c) the value of $f(2)$ is 0 which is equal to the obtained value and the value of $g(-2)$ is 0 which is also equal to the obtained value so this option is correct.

In the option (d), the value of $f(-2)$ is 0 but from the graph it can be observed that the value of $f(-2)$ is greater than 12, so this option is not correct.

Learn more:

1. Problem on Function https://brainly.com/question/1691598

2. How to solve Function https://brainly.com/question/1632445

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords:

Graphed function, f(0), f(2),g(0), f(x), g(x), intercept, intersection, axis, vertical, horizontal, lines, parabola function.