Question

For the function f(x) = $x^2$+6x+8 (6 marks) a) Complete the square and sketch the graph of the function f(x) by using transformation of graph. Show all steps involved. b) Find the image of the interval (-2; 2] c) Find the inverse image of the interval [-1; 3)

          For the function f(x) = $x^2$+6x+8
(6 marks)
a) Complete the square and sketch the graph of the function f(x) by using transformation of graph.
Show all steps involved.
b) Find the image of the interval (-2; 2]
c) Find the inverse image of the interval [-1; 3)

For the function f(x) = x^2+6x+8
(6 marks)
a) Complete the square and sketch the graph of the function f(x) by using transformation of graph.
Show all steps involved.
b) Find the image of the interval (-2; 2]
c) Find the inverse image of the interval [-1; 3)

Added by Carolyn G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Dr Harish Viswanathan

Step 1

To complete the square, we start by isolating the quadratic and linear terms: \[ f(x) = x^2 + 6x + 8 \] Next, we take the coefficient of $ x $, which is 6, divide it by 2, and square it: \[ \left( \frac{6}{2} \right)^2 = 9 \] We then rewrite the function by Show more…

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For the function f(x) = x^2 + 6x + 8 (6 marks), complete the square and sketch the graph of the function f(x) by using transformation of graph. Show all steps involved. Find the image of the interval (-2, 2]. Find the inverse image of the interval [-1, 3).