Question

Which of the following functions is graphed below?

Answer 1

Answer:

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line: $y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y=1(x+6)$

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

$f(x)=x^2+3$  

Piece-wise function

$f(x)=\left\{\begin{matrix}x^2+3&\ \ \text{ If }x>1\\x+6&\ \ \text{ If }x\leq 1\end{matrix}\right$

Please see the attached figure.

Hence, The option C is correct.

Answer 2

The third one ; ur welcome