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.
Find the range of this function:
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, . 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 is zero — that happens where — and there is no limit to how high can go, so ranges from 0 to infinity. Then its negative, ranges from negative infinity to 0.
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, , so the top of the range is 5.
So the range of is from negative infinity to 5. In other words, . In interval notation, that’s .
This question is similar to question number 11 in the sample questions for the Accuplacer Advanced Algebra and Functions test.