Question

Which graph represents a function that has the domain$(–\infty ,–4)\cup (–4,3)\cup (3,\infty )$, has a $y$-intercept at $(0,3)$, and is increasing on the interval $(0,4)$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Explanation of correct option:

Option(C):

The $y$-intercept of a graph is the point, where the graph crosses the $y$-axis.

Domain :

$(–\infty ,–4)\cup (–4,3)\cup (3,\infty )$

Graph in option(C) follow all given condition.

Hence, option(C) is correct.

Explanation of in-correct option:

Option(D):

From the list of given options. graph (D) has a $y$ intercept of $2$, because it crossed the $y$-axis at $y=2$.

So, graph (D) cannot be the required graph.

Option(A):

Graph (A) has a decreasing in $(0,4)$.

So, graph (A) cannot be the required graph.

Option(B):

The domain of graph (B) is $[-3,3]$

So, graph (B) cannot be the required graph.

Hence, the required graph is graph (C).