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Aneli [31]
3 years ago
7

Find the range of the function. f(x) = x2 + 3

Mathematics
2 answers:
Roman55 [17]3 years ago
5 0

Answer:

Range: [3,\infty)

Step-by-step explanation:

We have been given a function f(x)=x^2+3. We are asked to find the range of our given function.

We know that range of a function is values of dependent variable (y) for which function is defined.

We can see that our given parabola is in vertex form y=a(x-h)^2+K as y=1(x-0)^2+3 with a vertex at point (0,3).

Since our given parabola is an upward opening parabola, so point (0,3) is the minimum point.

We know that the range of an exponential function is form ax^2+bx+c with a vertex at (h,k) is:

If a>0, then range is f(x)\geq k

If a, then range is f(x)\leq k

Since the value of a is positive and k=3, therefore, the range of our given function would be f(x)\geq 3 that is [3,\infty).

Mama L [17]3 years ago
3 0

To find the range, you need to locate the vertex:

equation for vertex = ax^2 + bx +c

in x^2 + 3, a = 1, b = 0 and c = 3

now vertex form = a(x+d)^2 +e

d = b/2a = 0/2*1 = 0

e = c-b^2/4a = 3-0^2/4*1 = 3

The equation becomes: (x+0)^2 +3.


The range is Y ≥ 3 ( greater than or equal to 3)


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