# June 2010 Integrated Algebra Regents 11 – 14

11. (3) (the table with Quiz Average and Frequency)

“Bivariate Data”? They mean two variables. Frequency is just a count of averages, not a second variable. All the others – height and weight, gallons and miles, speed and distance, they all have two variable.

12. (3) c = 2, d = 2

You could graph both equations, if you are using the calculator, change c to y and d to x and transform the first to get y = -3x + 8 and y = 4x – 6, and see where they cross.

Or you could blog the cs and ds into both equations, and find the pair that works in both.

13. (4) The V-shaped graph (absolute value)

If it’s a function, each x goes with one y, or no ys, never more than one.

Putting it visually, if it is a function, a vertical line cannot hit it twice. And the other three fail that test.

14. (3) 3

A fraction is undefined if its denominator is 0.

You could plug each value in. Works fine.

or you could factor the denominator (x+3)(x-3) and realize that -3 or 3 will make the whole thing 0,

or you could graph y = (x – 2)/(x^2 – 9) and see where it “goes crazy” (gap or vertical asymptote).

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