y = -4x2 + 1 Range = {y:y=<1, y is an element of the reals}
The domain is from negative infinity to positive infinity. The range is from positive 2 to positive infinity.
A function is an equation that gives a unique answer. A relation does not. Example: y = 3x + 1 is a function. If I give you x, you can determine y. And that y is unique to that x. So if x = 1, you know y = 4. No other of x gives y = 4 as an answer. So y = 3x + 1 is a function. Example: y = 4x2. So if I give you x = 1, y = 4. But y = 4 if I also give you x = -1. So y = 4x2 is not a function, it is a relation.
yes!
The equation y = 4x^2 + 5 is a parabola
First you need to solve for y. So write 4x2+y=16 so y=16-4x2 Now write f(x)=16-4x2
y=4x2+3x+8
y = -4x2 + 1 Range = {y:y=<1, y is an element of the reals}
No. [ y = 4x2 ] is a quadratic equation.
yes
No.
The domain is from negative infinity to positive infinity. The range is from positive 2 to positive infinity.
y = 4x2 - 2 is a parabolic function with a focal point at the location (0, -2). It's derivative can be expressed as: dy/dx = 8x It's indefinite integral can be expressed as: ∫(4x2 - 2) dx = (4x3)/3 - 2x + C
y = 2 (4X2=8) +9 = 17
A function is an equation that gives a unique answer. A relation does not. Example: y = 3x + 1 is a function. If I give you x, you can determine y. And that y is unique to that x. So if x = 1, you know y = 4. No other of x gives y = 4 as an answer. So y = 3x + 1 is a function. Example: y = 4x2. So if I give you x = 1, y = 4. But y = 4 if I also give you x = -1. So y = 4x2 is not a function, it is a relation.
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Assuming the first function is y = 4x2 + 1, and the second y = 4x2 then the first graph is 1 unit higher than the second.
yes!