Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

the function f(x)=x^2+5x-6 is shifted 4 units to the left to create g(x). What is g(x)

Sagot :

xKelvin

Answer:

[tex]g(x) = x^2 + 13x + 30[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x) = x^2 + 5x - 6[/tex]

It is shifted 4 units left to create g(x), and we want to determine the equation of g.

Recall that to shift a function horizontally, we add a constant k to the function. k is the horizontal translation. That is:

[tex]\displaystyle f(x) \rightarrow f(x - k)[/tex]

Since we are shifting four units left, k = -4:

[tex]\displaystyle f(x) \rightarrow f(x - (-4)) = f(x+4)[/tex]

Find f(x + 4):

[tex]\displaystyle \begin{aligned} g(x) = f(x + 4) &= (x+4)^2 + 5(x+4) - 6 \\ \\ &= (x^2 + 8x + 16) + (5x + 20) - 6 \\ \\ &= (x^2) + (8x + 5x) + (16+20-6) \\ \\&= x^2 + 13x + 30\end{aligned}[/tex]

In conclusion:

[tex]g(x) = x^2 + 13x + 30[/tex]

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.