Question

Which is true regarding the graphed function f(x)? The graph is attached and the choices?

Answer 1

The right answer to the graph of the line with a negative slope is:

$f(5)=-1$

This is read as:

$f(x)=y=-1$

Then:

When $x$ is 5, the value of $y$ is $-1$

Answer 2

Answer: True statement is f(5) = -1

Step-by-step explanation:

According to the given graph,

f(x) is a linear function or a line.

Let the function f(x) is defined by,

f(x) = ax+b -------(1)

Where a and b are any numbers.

Since, f(x) is passes through the points (0,4) and (4,0),

Thus, (0,4) and (4,0) must satisfy f(x).

By putting (0,4) in equation (1),

4 = 0 x + b

⇒ 4 = b

Again by putting (4,0) in equation (1),

0 = 4 a + b

⇒ 0 = 4 a + 4

⇒ - 4 a = 4

⇒ a = - 1

By substituting the value of a and b in equation (1)

The given function is,

f(x) = - x + 4

For x = 0, f(0) = 0 + 4 ⇒ f(0) = 4

First option is incorrect.

For x = 5, f(5) = -5 + 4 ⇒ f(5) = -1

Second option is correct.

For x = 3, f(3) = -3 + 4 ⇒ f(3) = 1

Third option is incorrect.

For x = 2, f(2) = -2 + 4 ⇒ f(2) = 2

Fourth option is incorrect.