Algebra 2 Final Exam Prep

Match the sets of numbers in the different notations –3 < x < 3

• (-3,3)

• [-3,3)

• (-3,3]

• [-3,3]

Match the sets of numbers in the different notations. –3 ≤ x < 3

• (-3,3)

• [-3,3]

• [-3,3)

• (-3,3)

Match the sets of numbers in the different notations. –3 < x ≤ 3

• (-3,3)

• [-3,3)

• (-3,3]

• [-3,3]

Match the sets of numbers in the different notations. –3 ≤ x ≤ 3

• (-3,3)

• [-3,3)

• (-3,3]

• [-3,3]

draw a number line. closed circle at -6, open circle at 4. how's this written in interval notation?

• (-6,4]

• (–∞, 4]

• (–6, ∞)

• [–6, 4)

Match each set of numbers to the same set in interval notation. {x| x < –3}

• [-3,-1)

• (–∞, –3)

Match each set of numbers to the same set in interval notation. –3 < x ≤ –1

• (-3,-1]

• [-3,-1)

Match each set of numbers to the same set in interval notation. x ≥ –1

• [–1, ∞]

• [–1, ∞)

When looking at a table, how would you know if the relation is a function or not?

Answer explanation

If the x has more than 1 y value

Describe the changes that occur with the function g(x) = f (x + 4) – 6 compared to f(x). 

• Claim: g(x) takes f(x) and shifts it 4 units right and 6 units up. 

  Justification: Since down is negative in the vertical direction, this corresponds to a function that has a subtraction sign outside of the parentheses. Since left is horizontal and the negative direction, doing the opposite means this corresponds to a function which has an addition sign inside the parentheses.

• Claim: g(x) takes f(x) and shifts it 4 units left and 6 units down. 

  Justification: Since down is positive in the horizontal direction, this corresponds to a function that has a subtraction sign outside of the parentheses. Since left is vertical and the negative direction, doing the opposite means this corresponds to a function which has an addition sign inside the parentheses.

• Claim: g(x) takes f(x) and shifts it 4 units right and 6 units up. 

  Justification: Since down is negative, the opposite is up, so this corresponds to a function that has a subtraction sign outside of the parentheses. Since left is horizontal and the positive direction, this corresponds to a function which has an addition sign inside the parentheses.

• Claim: g(x) takes f(x) and shifts it 4 units left and 6 units down. 

  Justification: Since down is negative in the vertical direction, this corresponds to a function that has a subtraction sign outside of the parentheses. Since left is horizontal and the negative direction, doing the opposite means this corresponds to a function which has an addition sign inside the parentheses.