finding a function's range from its equation Archives • Jill Hacker

This post about finding a function’s range from its equation is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.

Question

Find the range of this function:

${\color{DarkBlue} y=-3x^4+5}$

Solution

A function’s range is the set of values y can take in that function.

You are asked to find a function’s range. What are the values y can take in this function?

Consider the first term, $-3x^4$ . Any real number (unless otherwise stated, it’s safe to assume x is real) to an even power, like 4, has a positive value or zero. It just can’t be negative. The lowest value of $3x^4$ is zero — that happens where $x=0$ — and there is no limit to how high $3x^4$ can go, so $3x^4$ ranges from 0 to infinity. Then its negative, $-3x^4$ ranges from negative infinity to 0.


$y=x^4$	$y=-x^4$	$y=-x^4+5$

The second term, 5. increases each y-value by 5. At the low end of the range, negative infinity plus 5 is still negative infinity, so the bottom of the range is still negative infinity. At the top end, $0+5=5$ , so the top of the range is 5.