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A student graphs the functions f(x) = | x+3 | and g(x) = x2-2x+3 on the coordinate plane shown.

Which are the solutions of f(x) =g(x)?

A. -3 and 1

B. -1 and 1

C. 0 and 3

D. 3 and 6

A student graphs the functions fx x3 and gx x22x3 on the coordinate plane shownWhich are the solutions of fx gx A 3 and 1 B 1 and 1C 0 and 3D 3 and 6 class=

Respuesta :

The solutions are the intersection point of both graphs

  • The left side graph is y=|x+3|
  • The right side top graph is x²-2x+3(Parabola)

So there mUST be two solutions

The intersections are

  • (0,3)
  • (3,6)

The x values are solution

  • They are 0,3

Option C

semsee45

Answer:

C. 0 and 3

Step-by-step explanation:

The solutions of f(x) = g(x) are the values of the x-coordinates of the points where the two graphed functions intersect.

From inspection of the graph, the points of intersection are:

  • (0, 3)
  • (3, 6)

Therefore, the solutions are 0 and 3 (since they are the x-values).

Proof

[tex]\implies f(x) = g(x)[/tex]

[tex]\implies |x + 3| = x^2-2x+3[/tex]

We only need to take the positive form of |x+3| since we can see from the graph that g(x) intersects f(x) when |x+3| is positive:

[tex]\implies x + 3 = x^2-2x+3[/tex]

[tex]\implies x^2-3x=0[/tex]

[tex]\implies x(x-3)=0[/tex]

[tex]\implies x=0, 3[/tex]

Thus confirming that the solutions are when x = 0 and 3

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