QuestionTranslate the function $f(x)=x^{3}$ right 1 unit and down 1 unit.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x^{3}$ . The function needs to be translated right by1 unit3. The function needs to be translated down by1 unit

STEP 2

To translate a function right by1 unit, we subtract1 from the input variable x in the function. This gives us a new function $g(x)$ .
$g(x) = f(x-1)$

STEP 3

Substitute $f(x)$ into the equation for $g(x)$ .
$g(x) = (x-1)^{3}$

STEP 4

To translate a function down by1 unit, we subtract1 from the entire function. This gives us the final transformed function $h(x)$ .
$h(x) = g(x) -1$

STEP 5

Substitute $g(x)$ into the equation for $h(x)$ .
$h(x) = (x-1)^{3} -1$ The function $f(x)=x^{3}$ translated right by1 unit and down by1 unit is $h(x) = (x-1)^{3} -1$ .

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QuestionTranslate the function $f(x)=x^{3}$ right 1 unit and down 1 unit.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x^{3}$ . The function needs to be translated right by1 unit3. The function needs to be translated down by1 unit

STEP 2

To translate a function right by1 unit, we subtract1 from the input variable x in the function. This gives us a new function $g(x)$ .
$g(x) = f(x-1)$

STEP 3

Substitute $f(x)$ into the equation for $g(x)$ .
$g(x) = (x-1)^{3}$

STEP 4

To translate a function down by1 unit, we subtract1 from the entire function. This gives us the final transformed function $h(x)$ .
$h(x) = g(x) -1$

STEP 5

Substitute $g(x)$ into the equation for $h(x)$ .
$h(x) = (x-1)^{3} -1$ The function $f(x)=x^{3}$ translated right by1 unit and down by1 unit is $h(x) = (x-1)^{3} -1$ .

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QuestionTranslate the function f(x)=x3f(x)=x^{3}f(x)=x3 right 1 unit and down 1 unit.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x3f(x)=x^{3}f(x)=x3 . The function needs to be translated right by1 unit3. The function needs to be translated down by1 unit

STEP 2

To translate a function right by1 unit, we subtract1 from the input variable x in the function. This gives us a new function g(x)g(x)g(x).g(x)=f(x−1)g(x) = f(x-1)g(x)=f(x−1)

STEP 3

Substitute f(x)f(x)f(x) into the equation for g(x)g(x)g(x).g(x)=(x−1)3g(x) = (x-1)^{3}g(x)=(x−1)3

STEP 4

To translate a function down by1 unit, we subtract1 from the entire function. This gives us the final transformed function h(x)h(x)h(x).h(x)=g(x)−1h(x) = g(x) -1h(x)=g(x)−1

STEP 5

Substitute g(x)g(x)g(x) into the equation for h(x)h(x)h(x).h(x)=(x−1)3−1h(x) = (x-1)^{3} -1h(x)=(x−1)3−1The function f(x)=x3f(x)=x^{3}f(x)=x3 translated right by1 unit and down by1 unit is h(x)=(x−1)3−1h(x) = (x-1)^{3} -1h(x)=(x−1)3−1.

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QuestionTranslate the function $f(x)=x^{3}$ right 1 unit and down 1 unit.

Assumptions1. The function is $f(x)=x^{3}$ . The function needs to be translated right by1 unit3. The function needs to be translated down by1 unit

To translate a function right by1 unit, we subtract1 from the input variable x in the function. This gives us a new function $g(x)$ .
$g(x) = f(x-1)$

Substitute $f(x)$ into the equation for $g(x)$ .
$g(x) = (x-1)^{3}$

To translate a function down by1 unit, we subtract1 from the entire function. This gives us the final transformed function $h(x)$ .
$h(x) = g(x) -1$

Substitute $g(x)$ into the equation for $h(x)$ .
$h(x) = (x-1)^{3} -1$ The function $f(x)=x^{3}$ translated right by1 unit and down by1 unit is $h(x) = (x-1)^{3} -1$ .