1. ## Domain and range (check my answers)

1) $\displaystyle y=5x-4$
D:all real no.
R:all real no.

2)$\displaystyle y=-x^2+7$
D:all real no.
R:all real no.

3)$\displaystyle y=\frac{5-x}{x-2}$
D:all real no. except 2
R: all real no.

4)$\displaystyle y=\sqrt{4-x}$
D:x<=4
R:all real no.

5)$\displaystyle y=\sqrt{x^2-16}$
D:-5<=x>=5
R:all real no.

6)$\displaystyle y=\sqrt{4-x^2}$
D:-2<=x<=2
R:0<=y<=2

7) $\displaystyle y=\sqrt{x^2-1}$
D:-1<=x>=1
R: all real no.

8)$\displaystyle y=^3\sqrt{x}-x$
D:all real no.
R:all real no.

9)$\displaystyle y=\frac{1}{x}$
D:all real no. except zero
R:all real no. except zero

10) $\displaystyle y=\frac{x}{x-2}$
D:x not = 2
R:y not = 1

(If any are wrong tell me which one and try solving it for me )
Thank you

2. Originally Posted by mj.alawami
1) $\displaystyle y=5x-4$
D:all real no. Correct
R:all real no. Correct

2)$\displaystyle y=-x^2+7$
D:all real no. Correct
R:all real no. Incorrect

3)$\displaystyle y=\frac{5-x}{x-2}$
D:all real no. except 2 Correct
R: all real no. Incorrect

4)$\displaystyle y=\sqrt{4-x}$
D:x<=4 Correct
R:all real no. Correct

5)$\displaystyle y=\sqrt{x^2-16}$
D:-5<=x>=5 Incorrect
R:all real no. Incorrect

6)$\displaystyle y=\sqrt{4-x^2}$
D:-2<=x<=2 Correct
R:0<=y<=2 Incorrect

7) $\displaystyle y=\sqrt{x^2-1}$
D:-1<=x>=1 Correct
R: all real no. Correct

8)$\displaystyle y=^3\sqrt{x}-x$
D:all real no. Correct
R:all real no. Correct

9)$\displaystyle y=\frac{1}{x}$
D:all real no. except zero Correct
R:all real no. except zero Correct

10) $\displaystyle y=\frac{x}{x-2}$
D:x not = 2 Correct
R:y not = 1 Incorrect

(If any are wrong tell me which one and try solving it for me )
Thank you
Have a go at fixing up these

3. Some corrections (in blue) to the corrections:

Originally Posted by mj.alawami
1) $\displaystyle y=5x-4$
D:all real no. Correct
R:all real no. Correct

2)$\displaystyle y=-x^2+7$
D:all real no. Correct
R:all real no. Incorrect

3)$\displaystyle y=\frac{5-x}{x-2}$
D:all real no. except 2 Correct
R: all real no. Incorrect

4)$\displaystyle y=\sqrt{4-x}$
D:x<=4 Correct
R:all real no. Correct Mr F says: The answer is incorrect. Draw the graph (it's the upper branch of a sideways parabola) ....

5)$\displaystyle y=\sqrt{x^2-16}$
D:-5<=x>=5 Incorrect
R:all real no. Incorrect

6)$\displaystyle y=\sqrt{4-x^2}$
D:-2<=x<=2 Correct
R:0<=y<=2 Incorrect Mr F says: The answer is correct. It's a semi-circle (upper half) of radius 2.

7) $\displaystyle y=\sqrt{x^2-1}$
D:-1<=x>=1 Correct Mr F says: The blue inequality is pointing the wrong way.
R: all real no. Correct

8)$\displaystyle y=^3\sqrt{x}-x$
D:all real no. Correct
R:all real no. Correct

9)$\displaystyle y=\frac{1}{x}$
D:all real no. except zero Correct
R:all real no. except zero Correct

10) $\displaystyle y=\frac{x}{x-2}$
D:x not = 2 Correct
R:y not = 1 Incorrect Mr F says: The given answer is correct. It's a hyperbola with horizontal asymptote y = 1 and vertical asymptote x = 2.

(If any are wrong tell me which one and try solving it for me )
Thank you
Originally Posted by Prove It
Have a go at fixing up these
..

4. Originally Posted by mr fantastic
Some corrections (in blue) to the corrections:

..
When I was trying to find the ranges, I checked the domains of the inverse functions. I stupidly forgot that the functions needed to be one-to-one to have inverses.