Question

4 from unit 5, lesson 4
function a gives the area, in square inches, of a square with side length x inches.
a. complete the table.

x	0	1	2	3	4	5	6
a(x)

b. represent function a using an equation.

c. sketch a graph of function a.
(graph: y - axis labeled area (square inches) with values 8, 16, 24, 32, 40, 48, 56; x - axis labeled side length (inches) with values 0,1,2,3,4,5,6,7,8)
5 from unit 5, lesson 5
function f is represented by f(x) = 5(x + 11).
a. find f(-2).

b. find the value of x such that f(x) = 90 is true.

Explanation:

Problem 4

Part a

Step1: Recall area of square formula

The area \( A \) of a square with side length \( x \) is \( A = x^2 \). So we calculate \( A(x)=x^2 \) for each \( x \).

Step2: Calculate for \( x = 0 \)

\( A(0)=0^2 = 0 \)

Step3: Calculate for \( x = 1 \)

\( A(1)=1^2 = 1 \)

Step4: Calculate for \( x = 2 \)

\( A(2)=2^2 = 4 \)

Step5: Calculate for \( x = 3 \)

\( A(3)=3^2 = 9 \)

Step6: Calculate for \( x = 4 \)

\( A(4)=4^2 = 16 \)

Step7: Calculate for \( x = 5 \)

\( A(5)=5^2 = 25 \)

Step8: Calculate for \( x = 6 \)

\( A(6)=6^2 = 36 \)

Step1: Recall area of square formula

The area of a square with side length \( x \) is the side length squared. So the function \( A(x) \) representing the area of a square with side length \( x \) is \( A(x)=x^2 \).

Step1: Substitute \( x=-2 \) into \( f(x) \)

We have the function \( f(x)=5(x + 11) \). Substitute \( x=-2 \) into the function.

Step2: Simplify the expression

\( f(-2)=5(-2 + 11)=5\times9 = 45 \)

Answer:

The completed table is:

\( x \)	0	1	2	3	4	5	6

Part b