# How do you find the domain and range of #y=2x^2+1#?

Domain: All real numbers

Range:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the domain and range of the function ( y = 2x^2 + 1 ), you need to consider the possible values of ( x ) that the function can take and the corresponding values of ( y ).

- Domain: The domain of the function is all real numbers because there are no restrictions on the values that ( x ) can take.

[ \text{Domain} = (-\infty, +\infty) ]

- Range: To find the range, you need to consider the behavior of the function. Since the coefficient of ( x^2 ) is positive (2 in this case), the function opens upwards, and its minimum value occurs at the vertex of the parabola. The vertex of the parabola is at the point ((h, k)), where (h = -\frac{b}{2a}) and (k) is the value of the function at (h). In this case, (a = 2), (b = 0), and (c = 1).

[ h = -\frac{b}{2a} = -\frac{0}{2(2)} = 0 ] [ k = 2(0)^2 + 1 = 1 ]

So, the vertex is at ((0, 1)). Since the parabola opens upwards, the range is all real numbers greater than or equal to the (y)-coordinate of the vertex.

[ \text{Range} = [1, +\infty) ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the domain of #(3x^2+3x-6)/(x^2-x-12)#?
- Tape travels through a tape player at a speed of 9.45 ft per min How many feet of tape are needed for half an hour of continuous music?
- How do you find the domain and range of #f(x)=x^2+5#?
- The sum of two numbers is 12 Their difference is 4. How do you find the numbers?
- The sum of four consecutive integers is 2174. How do you find the numbers?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7