Suppose that H(x)= (1/5)* -3125.

(a) What is H(-6)? What is the point that corresponds to this value on the graph of H?

(b) If H(x)=-2500, what is x? What is the point that corresponds to this value on the graph of H?

(c) Find the zero of H.

(a) H(-6)=(Type an integer or a simplified fraction.)

The point that corresponds to this value on the graph of H is (Type an ordered pair, but do not use commas in any individual coordinates.)

(b) If H(x) = -2500, then x=(Type an integer or a simplified fraction.)

The point that corresponds to this value on the graph of H is (Type an ordered pair, but do not use commas in any individual coordinates.)

(c) The zero of H is x=

(Type an integer or a simplified fraction.)

H(-6) = -625, the corresponding point on the graph is (-6, -625). H(x) = -2500, x = 4, the corresponding point on the graph is (4, -2500). Zero of H is x = 0.

Explanation:

(a) To find the value of H(-6), substitute -6 into the function H(x) = (1/5) * -3125:
H(-6) = (1/5) * -3125 = -625. The point that corresponds to this value on the graph of H is (-6, -625).
(b) To find the value of x for H(x) = -2500, set H(x) equal to -2500 and solve for x:
-2500 = (1/5) * -3125. Multiplying both sides by 5, we get -12500 = -3125x. Dividing both sides by -3125, we find that x = 4. The point that corresponds to this value on the graph of H is (4, -2500).
(c) To find the zero of H, we need to find the value of x when H(x) = 0:
0 = (1/5) * -3125. Multiplying both sides by 5, we get 0 = -3125x. Dividing both sides by -3125, we find that x = 0.

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