Question

The function f(x) = (x − 4)(x − 2) is shown. On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0). What is the range of the function? all real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1 Mark this and return Save and Exit Next

Answer 1

Explanation:

all real numbers greater than our equal to -1.

as the parabola function is y = something in x², the parabola opens up either up or down.

if the function would have been x = something in y², the parabola would open left or right.

but our parabola here opens therefore up and down.

the vertex is therefore the maximum or minimum of the parabola. y does not get larger or smaller than the y value of the vertex.

as we see that the curve goes through points with y value 0 (which is clearly larger than -1), it means the vertex is a minimum, and the parabola opens up.

therefore the answer at the beginning. any y value of the function can only be greater than or equal to -1.