Chapter 1 & 2
Function and image
The function f(x)=4+x2 is given
Filling in x=6 in the function gives f(6)=4+62 or f(6)=40
By rewriting the formula a+4b=12 as b=-0.25a+3 ( : the whole function by 4)
Linear, quadratic and constant function
Linear : F(x)= -x+1
Quadratic : F(x)=-x2+5
Constant : F(x)= 2
Domain and range
The function F(x)=2- x-3 only has results when x is greater than or equal to 3.
The domain of F is x> 3
The images of function F are smaller or equal to 2.
The range of F is y<2
You can fill in different numbers for the parameter a in F(x)= a x-3
A family of graphs
Directly proportional and constant of proportionality
For image, see attachment!
Directly proportional: When a variable x is multiplied by 2, the variable y also becomes 2x as large, so x and y are directly proportional.
Constant of proportionality: The formula y=cx, where c is called constant op proportionality. Therefore the gradient of the corresponding line is the constant of proportionality.
Fractional function, hyperbola, horizontal and vertical asymptote
Fractional function: f(x)= 6:x+3
Hyperbola: The graph of a fractional function.
Asymptote: when a graph has two branches and one number will never be included in the domain of this function.
Here the horizontal and the vertical asymptotes are 0.
Upward and downward opening parabolas
Upward: When it’s positive = x2
Downward: When it’s negative = -x2
How do you find the coordinates of the vertex?
1. Find the 2 x-values that have the same y-value. These could be the points of intersection with the x-axis.
2. The x-value of the axis of symmetry of the parabola lies in the middle between the two x-values you found.
3. Calculate the y-value of the vertex by substituting the x-value of the axis of symmetry into this function.
4. Write down the coordinates of the vertex.
How do you plot a parabola?
1. Calculate the coordinates of the vertex.
2. Make a table and include the x-value of the vertex.
3. Make a coordinate system with a suitable scale on the axes.
4. Plot the graph.