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In any function, f(x) = a(x-h)n + k , a negative leading coefficient means the graph is reflected. True or False

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Answer:

True

Explanation:

For any function of the form
f(x) = a(x-h) ^ n + k the coefficient a produces a reflection of the function whenever
a <0.

We can verify it in the following way.

Take, for example, the function:


f(x) = 2(x-1) ^ 3

Now let's make
f(2)


f(2) = 2(2-1)^3\\\\f(2) = 2

Now let's
f(2) in the following function:


f(x) = -2(x-1)^3

We have:


f(2) = -2(2-1)^3\\\\f(2) = -2

We can see then that the function was reflected in the axis -y by placing a negative coefficient a.

You can see more examples in the attached images

Therefore we can conclude that the statement is true.

In any function, f(x) = a(x-h)n + k , a negative leading coefficient means the graph-example-1
In any function, f(x) = a(x-h)n + k , a negative leading coefficient means the graph-example-2
User GWu
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