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Write the equation for
g that represents the indicated transformation of the graph
f.
f(x)=log x; translation 3 units to the left and 2 units up, followed by a reflection in the
x axis

Write the equation for $g$ that represents the indicated transformation of the graph $f$ . $f(x)=\log x$ ; translation $3$ units to the left and $2$ units up, followed by a reflection in the $\mathrm{x}$ axis

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Transformations of functions

Full solution

Q. Write the equation for

g

that represents the indicated transformation of the graph

f

.

f(x)=\log x

; translation

3

units to the left and

2

units up, followed by a reflection in the

\mathrm{x}

axis

Replace $x$ with $(x + 3)$ : To translate the function $3$ units to the left, we replace $x$ with $(x + 3)$ in the function $f(x) = \log x$ . This gives us the intermediate function $h(x) = \log(x + 3)$ .
Translate $2$ units up: Next, we translate the function $h(x) = \log(x + 3)$ $2$ units up by adding $2$ to the function. This gives us the intermediate function $i(x) = \log(x + 3) + 2$ .
Reflect in x-axis: Finally, to reflect the function $i(x) = \log(x + 3) + 2$ in the x-axis, we multiply the function by $-1$ . This gives us the final function $g(x) = -\log(x + 3) - 2$ .

More problems from Transformations of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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What does the transformation

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\text{translates it } 4 \text{ units right}

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\text{translates it } 4 \text{ units down}

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\text{translates it } 4 \text{ units left}

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\text{translates it } 4 \text{ units up}

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What does the transformation

f(x) \mapsto f(4x)

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[A] stretches it vertically

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[B] stretches it horizontally

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[C]shrinks it horizontally

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[D]shrinks it vertically

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Question

g(x)

g(x)

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f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

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g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

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Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

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\text{[D]translation 10 units right}

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Question

y=x^{2}

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y=

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Question

y=x^{2}

is shifted down by

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units and to the right by

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What is the equation of the new parabola?

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y=x^{2}

is shifted up by

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What is the equation of the new parabola?

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Question

y=x^{2}

is reflected across the

x

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5

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What is the equation of the new parabola?

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y=\square

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Question

y=x^{2}

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What is the equation of the new parabola?

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y=

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