Results are out! Find what you Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

C3 functions help please!

Announcements Posted on
Let our uni choice search tool match you with your perfect university 19-11-2015
  1. Offline

    we have just started learning about functions but i don't entirely understand and if anyone could help on these questions i would really appreciate it!
    1)if you have the graph f(x)=^3,with domain x is a real number (cant draw it on here!), then what would the range be? would it be f(x) is a real number?
    also, if you had the same graph but domain x>2, would the range be f(x)>8?

    2) how do you find the range for (x-2)^2 + 3 where x is a real number?

    i'm not really certain about this topic so pleaseeee help if you can thankyou!
  2. Offline

    1) First one is a cubic, and you should know that the domain and range of any odd-degree polynomial (with no constraints) is all real numbers. So yeah, f(x) is a real number.

    You're also right for f(x)>8. As x increases (from 2), f(x)=x^3 increases, so there's no way to get under 2^3. Also, as x tends to infinity, so does x^3.

    2) There are two ways to interpret the quadratic:

    Vertex form: A quadratic, when put in the form a(x-h)^2+k, has a vertex at (h,k). If a is positive, it opens up, and if a is negative, it opens down.
    For (x-2)^2 + 3, a=1, h=2, and k=3. So this quadratic is a parabola that opens up with a vertex at (2,3). Recall that the vertex is always the minimum/maximum of a quadratic.

    Transformations: f(x)=x^2 is a function with a range of x≥0 (so the minimum is at 0). f(x)+k is a function that is moved up by 'k' units. Therefore, the minimum is also moved up by 'k' units.


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: June 18, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Today on TSR

Applying to uni

The latest advice and trending discussions are all here

What's your favourite kitchen utensil?
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.