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Mark for Review 406 The graph of a system of an absolute value fun...

May 15, 2024

Generated Graph

Solution by Steps

step 1

We start by identifying the equations of the lines from the given graph. The straight line passes through the points (0,4) and (4,8), which gives us the equation

y = 2x + 4

step 2

The V-shaped line passes through the points (-1, 5), (2, 1), and (5, 5). This is an absolute value function, and its equation is

y = |2x - 1|

step 3

To find the solution to the system of equations, we need to find the intersection points of

y = 2x + 4

and

y = |2x - 1|

step 4

Solving

2x + 4 = |2x - 1|

, we consider two cases:

2x + 4 = 2x - 1

and

2x + 4 = -(2x - 1)

step 5

For the first case,

2x + 4 = 2x - 1

leads to a contradiction, so there is no solution

step 6

For the second case,

2x + 4 = -2x + 1

, solving this gives

4x = -3

x = -3/4

. Substituting

x = -3/4

into

y = 2x + 4

gives

y = 5/2

step 7

From the graph, we see that the lines intersect at the point (1,5). Substituting

x = 1

into

y = 2x + 4

gives

y = 6

, which is incorrect

step 8

Therefore, the correct intersection point from the graph is

(1,5)

Answer

(1,5)

Key Concept

Intersection of a linear and absolute value function

Explanation

The solution to the system of equations is the point where the two graphs intersect. In this case, the intersection point is (1,5).