Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is an equation for g(x)?

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Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is an equation for g(x)?

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Answer 1 · 2017-03-04T15:49:16

$g (x) = 32 x - 7$ $g(x) = 32x - 7$

Explanation:

In $y = a f b (x + c) + d$ $y = afb(x + c) + d$ :

• $a$ $a$ represents the vertical stretch

• $b$ $b$ represents the horizontal stretch

• $c$ $c$ represents the horizontal translation

• $d$ $d$ represents the vertical translation

We are given that $g (x)$ $g(x)$ has a vertical stretch and a vertical translation (down and up are on the y-axis, hence it's a vertical translation).

Therefore, the equation of $g (x)$ $g(x)$ is

$g (x) = 4 (8 x) - 7 = 32 x - 7$ $g(x) = 4(8x) - 7 =32x - 7$

Practice Exercises

Consider the function $f (x) = x^{3}$ $f(x) = x^3$ . $f (x)$ $f(x)$ undergoes a vertical transformation of $5$ $5$ units down and a horizontal translation of $2$ $2$ units right. It is reflected over the x-axis. What is $f (x)$ $f(x)$ 's new equation?
The point $(6, - 4)$ $(6, -4)$ lies on the graph of function $g (x)$ $g(x)$ . What are the coordinates of the point that will lie on $2 g (3 x - 9) + 1$ $2g(3x - 9) + 1$ ?

Solutions

$f (x) = - {(x - 2)}^{3} + 2$ $f(x) = -(x - 2)^3 + 2$
$(5, - 7)$ $(5, -7)$

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Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is an equation for g(x)?

1 Answer

Explanation:

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