Answer:
G(-1, 3)
Step-by-step explanation:
You need to try each point in the given equation to see which one does not work.
The definition of the function is that it has two different expressions. The upper expression is used for values of x that are less than or equal to -1.
For values of x less than or equal to -1, the expression is f(x) = 2x + 3.
Look at point F. Its x-coordinate is -1.5. Since -1.5 is less than or equal to -1, use the upper expression. Plug in -1.5 for x and find f(-1.5).
f(x) = 2x + 3
f(-1.5) = 2(-1.5) + 3 = -3 + 3 = 0
That gives point (-1.5, 0), so point F is on the graph of f(x).
Now let's look at point G(-1, 3). For point G, x is -1. Since -1 is also less than or equal to -1, you still use the upper expression for x = -1.
f(x) = 2x + 3
f(-1) = 2(-1) + 3 = -2 + 3 = 1
The point that contains x-coordinate -1 is point (-1, 1). Point G is (-1, 3), so point G is not on the graph of function f.
You already know the answer is point G, but let's continue to show how the other two points are part of the graph of the function.
Point H is (0, 4). For this point, the x-coordinate is 0. The lower expression is used for x greater than -1, and 0 is greater than -1, so you must use the second expression. Now we evaluate the function at x = 0 using the second expression.
f(x) = 4 + x
f(0) = 4 + 0 = 4
giving us point (0, 4).
Point H is (0, 4), so point H is on the graph of the function.
Now we do point J(4, 8). Like for point H, the x-coordinate of point H is greater than -1, so you use the second expression.
f(x) = 4 + x
f(4) = 4 + 4 = 8
giving point (4, 8).
Point J is (4, 8), so it is on the graph.
The only point not on the graph is point G.
Answer: G(-1, 3)
