How do you describe the transformation of $f (x) = x^{3} + 7$ $f(x)=x^3+7$ from a common function that occurs and sketch the graph?

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Answer 1 · 2017-12-06T09:17:44

see below

in general if the function $f (x)$ $" "f(x)" "$ is translated by the vector

$((a),(b))" "$

then the equation of the transformed function is $" "f(x-a)+b$

we ae given

$f(x)=x^3+7$

comparing this to the general form we have

$f(x)=x^3+7" is a translation of " f(x)=x^3" by the vector "$

$((0),(7))$

see the graphs below

graph{x^3 [-10, 10, -5, 5]}

$f(x)=x^3$

graph{x^3+7 [-58.5, 58.54, -29.27, 29.3]}

$f(x)=x^3+7$

How do you describe the transformation of f(x)=x^3+7f(x)=x3+7f(x)=x^3+7 from a common function that occurs and sketch the graph?