Home->ACT Math

The graph of y = f(x) is shown in the standard (x,y) coordinate plane below with points V, W, X, Y, and Z labeled.

 

If y = f(x) is to be reflected across the line y = x, which of the following graphs represents the result?

(A)

(B)

(C)

(D)

(E)

For which of the following values of a will there be exactly one real solution to the equation 2x² - ax + 8 = 0?

（A）2 （B） 4 （C） 4 （D） 6 （E） 8

Correct Answer: E

A function is defined for x and y such that f_{(x, y)} = -2xy + y + x - 4. So, for x = 2 and y = 3, f_{(2, 3)} = -2 × 2 × 3 + 3 + 2 - 4 = -12 + 1 = -11. If x and y are to be chosen such that f_(x,y) = f_(y,x), then which of the following restrictions must be placed on x and y?

(F) x > 0 and y > 0 (G) x < 0 and y < 0 (H) x = y (J) xy < 0 (K) No restrictions are needed.

Correct Answer: K

An integer from 299 through 1,000, inclusive, will be chosen randomly. What is the probability that the number chosen will have 1 as at least 1 of its digits?

（A） （B） （C） （D） （E）

Correct Answer: B