Math methods units 1&2 help

[Rose34]

Sketch the graphs of each of the following and state the range of each:
y = x^2 + 3, x∈[−1,1]

My working out:
I subbed in -1 and 1 as x in the equation but that did not work.
y=(-1)^2 +3
y=4

Then
y=(1)^2+3
y=4

Thus the range is [4,4]

But the answer is:  [3,4]

[Evolio]

Hello!
Ah, so for this question you had to take into account the turning point. Since it's not a linear graph but a parabola, it is useful to sketch the graph so that you can easily see where the lowest point of the graph is and where the highest point is.
By looking at the graph, we can see that the turning point is (0,3) and the highest point from subbing either -1 or 1 is 4. Thus the range is [3,4]
Here is the graph for reference.

[BiggestVCESweat]

Sketch the graphs of each of the following and state the range of each:
y = x^2 + 3, x∈[−1,1]

My working out:
I subbed in -1 and 1 as x in the equation but that did not work.
y=(-1)^2 +3
y=4

Then
y=(1)^2+3
y=4

Thus the range is [4,4]

But the answer is:  [3,4]

To find the range of a continuous function, find the values of the endpoints (or the limits) of the endpoints and the values of the points where the derivative is 0.

In this case the derivative is 0 when x=0, and y=3 when x=0. (The endpoints are (-1,4) and (1,4) as you stated.)

Hence the range is [3,4]

[Rose34]

Thanks for the help!!