HELP! PLEASE! which graph represents a function? How do you know?

Mathematics

2 answers:

Andreas93 [3]4 years ago

5 0

I agree the answer is D

WITCHER [35]4 years ago

4 0

Any graph will represent a function if it passes the vertical line test. A graph is a function if for any vertical line drawn it touches the graph at only one point.In other words for every x there is only one y value.

In the given graphs if a vertical line is drawn in the graphs A,B it will touch the graph at two points and hence they are not unctions.Option c s a vertical line that is for one x value there are more than one value of y and so is not a function.Option D will represent a function as any vertical line drawn will touch the graph at only one point.

OPtion D.

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Find the vertex of the graph of f(x) = x2 + 4x - 5.

Fofino [41]

You can solve this in two ways.

1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.

2. Analytical. Calculate the derivative of the function f(x)
$\frac{df}{dx}=2x+4$
Solve the equation:
$2x+4=0$
will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:
$(-2)^2+4 \cdot (-2)-5=4-8-5=-9$

You get the same answer: x=-2, y=-9

So the answer is
B. (-2, -9)