# Thread: Graph of a function

1. ## Graph of a function

1. Write down the range of values of x for which the graph of y = f(x) has a negative gradient.
I don't even know where to start with the first step.

2. The equation f(x) + x – 1 = 0 can be solved by drawing a line on the grid.

(i) Write down the equation of this line. [1]

(ii) How many solutions are there for f(x) + x – 1 = 0?
They're talking about a tangent line, yes? So where do I draw it?

2. negative gradient $x \in (0,6)$

Can you see why?

3. I think its because the gradient between y=0 and y=6 is sloping downwards to the right?

4. Q1

x=0 to x=6

Q2

y=-x+1

get some points for the line,
x=0, y=1
x=1, y=0

plot the line then count number of intersection points.

5. Oh ok thanks I understand Q. 2, however I'm still stuck with Q. 1.

6. Originally Posted by yorkey
I think its because the gradient between y=0 and y=6 is sloping downwards to the right?
What is the definition of a negative gradient? Surely your text tells you that much?

-Dan

7. Originally Posted by topsquark
What is the definition of a negative gradient? Surely your text tells you that much?

-Dan
A negative gradient slopes down and to the right. Actually, I think I get it now.

"...graph of y = f(x) has a negative gradient. " There's only one negative slope, so the answer is the start and end values of the slope on the x-axis. The slope starts at (0,3) and ends at (6,-9) so the answer is 0 and 6. Is my reasoning right?

8. Originally Posted by yorkey
A negative gradient slopes down and to the right. Actually, I think I get it now.

"...graph of y = f(x) has a negative gradient. " There's only one negative slope, so the answer is the start and end values of the slope on the x-axis. The slope starts at (0,3) and ends at (6,-9) so the answer is 0 and 6. Is my reasoning right?
Yup!

-Dan

9. Awesome, you guys rock.