Question

The function f(x) is shown in the graph.

What is the equation forf(x)?



Enter your answer in the box.

f(x)=

Answer 1

Given:-

• A graph of a function is given to us .

To find:-

• The function.

Answer:-

From the graph, we can see that it passes through the points (0,-3) and (-5,1) . Using these two points,we can find the slope of the line as ,

`\implies m =(y_2-y_1)/(x_2-x_1) \\`

And here ,

• 
  `x_1 = 0`
• 
  `x_2 = -5`
• 
  `y_1 = -3`
• 
  `y_2 = 1`

So , on substituting the respective values, we have;

`\implies m =(1-(-3))/(-5-0) \\`

`\implies m = ( 1+3)/(-5) \\`

`\implies m =-(4)/(5) \\`

Here the graph , cuts the y axis at (0,-3) . So the y- intercept of the graph is -3 . Now we may use the slope intercept form of the line to find the function . The slope intercept form of the line is
`y = mx + c` , where ;

• 
  `c` is y intercept
• 
  `m` is the slope.

And here ,

• 
  `m =-(4)/(5)`
• 
  `c = -3`

Again, on substituting the respective values, we have;

`\implies y = (-4)/(5)x + (-3) \\`

`\implies y =(-4)/(5)x - 3 \\`

Replace
`y` with
`f(x)`

`\implies \underline{\underline{ f(x) =-(4)/(5)x -3}} \\`

This is the required function of the given graph .

And we are done!