Question

Consider the graph of the function $F$ defined by $F(x) = |2x| + 4$ for all numbers $x$ . For which of the following functions $G$ defined for all numbers $x$ does the graph of $G$ intersect the graph of $F$ ?

A.
$G(x) = x + 3$
B.
$G(x) = 2x - 2$
C.
$G(x) = 2x + 3$
D.
$G(x) = 3x - 2$

Accepted Answer

D. For $G(x) = 3x - 2$: Case $x \ge 0$: $F(x) = 2x + 4$. Equating $2x + 4 = 3x - 2 \Rightarrow x = 6$. Since $x = 6 \ge 0$, this is a valid point of intersection. Thus, $G(x) = 3x - 2$ intersects $F(x)$.

Intersection of Functions and Graphs

Explanation

Practise this under exam conditions