For each of the functions below, state the domain and range, the restrictions, the intervals of increasing and decreasing, the roots, y-intercepts, and vertices.
1) f(x)=2x^2−8
2) f(x)=+√x - 2
3) f(x)=x+1/x-1
+118696 ok I will take a look :))
For each of the functions below, state the domain and range, the restrictions, the intervals of increasing and decreasing, the roots, y-intercepts, and vertices.
1) f(x)=2x^2−8
2) f(x)=+√x - 2
3) f(x)=x+1/x-1
1)f(x)=2x2−8
Any real number can be squared so x can be any real number
Domain: x∈R (x is in the set of reals) (−∞,∞)
x2 cannot be negative, it can be any positive number though. Same for 2x2
2x2−8 cannot be any smaller than -8
Range: −8≤f(x)<∞[−8,∞)
Even before you went to all this bother you should have recognised that this is a concave up parabola.
It is a steeper version of y=x^2 And every point is dropped 8 units.
In other words, The axis of symmetry is x=0 (That is the y axis)
The vertex is (0,-8)
The y intercept is -8
It is decreasing when x
It is increasing when x>0 (the tangent has a positive gradient)
When f(x)=0
0=2x2−80=x2−40=(x−2)(x+2)x−2=0orx+2=0x=2orx=−2$Therootsarex=2andx=−2$
I think that covers the first one.
Think about it and aske questions if you have any.
Have a go at the second one yourself and present what you think.
Here is the graph:
https://www.desmos.com/calculator/gmxuxxwtbv
I will talk about it with you then :)
+118696 ok I will take a look :))
For each of the functions below, state the domain and range, the restrictions, the intervals of increasing and decreasing, the roots, y-intercepts, and vertices.
1) f(x)=2x^2−8
2) f(x)=+√x - 2
3) f(x)=x+1/x-1
1)f(x)=2x2−8
Any real number can be squared so x can be any real number
Domain: x∈R (x is in the set of reals) (−∞,∞)
x2 cannot be negative, it can be any positive number though. Same for 2x2
2x2−8 cannot be any smaller than -8
Range: −8≤f(x)<∞[−8,∞)
Even before you went to all this bother you should have recognised that this is a concave up parabola.
It is a steeper version of y=x^2 And every point is dropped 8 units.
In other words, The axis of symmetry is x=0 (That is the y axis)
The vertex is (0,-8)
The y intercept is -8
It is decreasing when x
It is increasing when x>0 (the tangent has a positive gradient)
When f(x)=0
0=2x2−80=x2−40=(x−2)(x+2)x−2=0orx+2=0x=2orx=−2$Therootsarex=2andx=−2$
I think that covers the first one.
Think about it and aske questions if you have any.
Have a go at the second one yourself and present what you think.
Here is the graph:
https://www.desmos.com/calculator/gmxuxxwtbv
I will talk about it with you then :)
