(g(1) = 10 (g(n) = g(n − 1) – 7.5 g(3) =

Mathematics

1 answer:

Amanda [17]3 years ago

5 0

Answer:

g(3) = - 5

Step-by-step explanation:

Given

g(n) = g(n - 1) - 7.5 and g(1) = 10, then

g(2) = g(2 - 1) - 7.5 = g(1) - 7.5 = 10 - 7.5 = 2.5

g(3) = g(3 - 1) - 7.5 = g(2) - 7.5 = 2.5 - 7.5 = - 5

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Given a quadratic function in vertex form:

Alja [10]

Answer:

See below

Step-by-step explanation:

Part A

A vertical stretch takes place when $a\cdot f(x)$ given that $|a| > 1$

Part B

A vertical compression takes place when $a\cdot f(x)$ given that $0 < |a| < 1$

Part C

A vertical stretch is different than a horizontal compression:

In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

Part D

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of $a$ must be negative such that $a\cdot f(x)$ as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.