What is the range of y=-2x^4 + 7. Please, step by step solving so I may understand.

Answer 1

The range is the output or y-value, right?

Because we have an even exponent, no matter what value for x we put in (other thsn 0) will be positive 5(5)(5)(5) = -5(-5)(-5)(-5) for example.

Multiplying by -2, though, will make -2x⁴ negative, however.

The exception bein x = 0. Then y = 7. Because -2x⁴ will otherwise be negative, adding 7 will always be less than 7.

Soooooo, the range is y ≤ 7, as no value of x will give us a y-value greater than 7.

Answer 2

First, determine if there are any discontinuities. Since we never divide by an x term, we never wind up dividing by zero, so the expression is well-behaved for all values of x.

Next, note what simplifications can be made for large x values. In this case, the expression simply becomes -2x⁴. This will be negative for all x values, and will increase to negative infinity.

Finally, find the maximum positive value. As x approaches zero, the expression simply becomes 7.

The range of y is therefore defined as: y ≤ 7

I recommend using a graphing tool to help visualize these problems. Here is one good one:

https://www.desmos.com/calculator

Answer 3

I graphed it. rise/run=-1510/-5 and -1510/5.