Question

Please help I don’t know how to do this

Answer 1

Answer:

f(x) = -2x + 7, when x > 1

f(x) = 4x + 1 when x ≤ 1

Step-by-step explanation:

The right side graph passe through points (1,5) and (2,3).  

Hence, the equation of the line  

$\frac{y - 5}{5 - 3} = \frac{x - 1}{1 - 2}$

⇒ (y - 5) = 2(1 - x)

⇒ y - 5 = 2 - 2x

⇒ y = -2x +7.......... (1)

Now, the left side graph passes through points (1,5) and (0,1)

Therefore, the equation of the graph will be  

$\frac{y - 5}{5 - 1} = \frac{x - 1}{1 - 0}$

⇒ y - 5 = 4(x - 1)

⇒ y = 4x + 1 ........ (2)

Hence, the equation (1) gives the function in the right side of the given graph which does not include the point (1,5) and extends to the right from this point.

Therefore, f(x) = -2x + 7, when x > 1 (Answer)

Again, equation (2) gives the function in the left side of the given graph which includes the point (1,5) and extends to the left from this point.

Therefore, f(x) = 4x + 1 when x ≤ 1 (Answer)