Determine the wheather the equation y as a function of x
X^2+y=25
X+y^2=25
X=y^2
The equation y as a function of x can be determined by solving each equation separately for y.
1) X^2 + y = 25:
To solve for y, subtract X^2 from both sides:
y = 25 - X^2
2) X + y^2 = 25:
To solve for y, take the square root of both sides:
√(X + y^2) = √25
y = ±√(25 - X)
3) X = y^2:
Solving for y, take the square root of both sides:
√X = y
Therefore, y as a function of x is given by:
y = 25 - X^2 (from equation 1)
y = ±√(25 - X) (from equation 2)
y = √X (from equation 3)
To determine the relationship between x and y in each equation, we can solve them step-by-step.
1. Equation: X^2 + y = 25
Step 1: Move the y term to the other side of the equation.
X^2 = 25 - y
Step 2: Take the square root of both sides to solve for x.
√(X^2) = √(25 - y)
Step 3: Simplify the equation.
|x| = √(25 - y)
So, x can be expressed as ±√(25 - y). The relationship between x and y is not a function since for each value of y, there are two possible values of x.
2. Equation: X + y^2 = 25
Step 1: Move the x term to the other side of the equation.
y^2 = 25 - x
Step 2: Take the square root of both sides to solve for y.
√(y^2) = √(25 - x)
Step 3: Simplify the equation.
|y| = √(25 - x)
Similar to the previous equation, y can be expressed as ±√(25 - x). The relationship between y and x is not a function.
3. Equation: X = y^2
This equation represents a parabola. For each value of y, there is only one corresponding value of x. Thus, this equation represents y as a function of x.