1.What is the shape of the graph of any linear function?

Answer-line

2. Solve for x in |5x -2| >5
Answer- 2/3 < x <1

3. Compare the quantity in Column A with the quantity in Column B.

Column A
x + 12

Column B
12 + x
Answer-The two quantities are equal

4. Write a function rule for the table shown

X 3 4 5 6
F(x) 9 16 25 36
Answer-f(x)=x^2

5. Given f(x) x^3 -3 find f(-2).
Answer-f(x)= -11

number two:

check your answers. if x=1/2 :(less than one)

abs(5*1/2 -2)>5 ?
abs(5/2-2)>5
abs(.5) which is NOT greater than 5

Sorry, I wrote the answer wrong.

3/5 < x < 1

Are the rest correct?

1. The shape of the graph of any linear function is a straight line. To understand this, you can consider the general form of a linear function, which is y = mx + b, where m represents the slope (steepness) of the line, and b represents the y-intercept (the point where the line crosses the y-axis). Since the graph follows a straight line, it implies that for any change in x (horizontal axis), there is a corresponding proportional change in y (vertical axis).

2. To solve the inequality |5x-2| > 5, you can follow these steps:
a) Set up two separate equations:
i) 5x-2 > 5
ii) 5x-2 < -5
b) Solve each equation separately:
i) For 5x-2 > 5, add 2 to both sides and divide by 5 to get x > 7/5, which simplifies to x > 1.4.
ii) For 5x-2 < -5, add 2 to both sides and divide by 5 to get x < -3/5, which simplifies to x < -0.6.
c) Combine the two solutions: -0.6 < x < 1.4. So, 2/3 < x < 1.

3. When comparing the quantities in Column A and Column B (x + 12 vs. 12 + x), you can see that the algebraic form of both expressions is the same. Thus, the two quantities are equal. This is because the commutative property of addition states that changing the order of the terms does not affect the sum.

4. Given the table:
X 3 4 5 6
F(x) 9 16 25 36

To find the function rule, observe the pattern of the outputs (F(x)) in relation to the inputs (x). Looking at the table, you can notice that the outputs are the squares of the inputs. Thus, the function rule can be written as f(x) = x^2. This means that you can square any value of x to find the corresponding output.

5. Given the function f(x) = x^3 - 3, you need to find f(-2). To do this, substitute -2 into the function and evaluate the expression. Plug in -2 for x:
f(-2) = (-2)^3 - 3
= -8 - 3
= -11. So, f(-2) equals -11.