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Copy/Paste Formulae for Chapter 1 Relations and Functions

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Handy Shortcuts

Shift+Enter to execute a command
Ctrl-s save your file
Alt+7 to start a text cell
Ctrl-/ gives a fraction (□/□)
Ctrl-2 gives a square root sign (Sqrt[□])
Ctrl-6 gives an exponent (□^□)

All Mathematica commands start with a Capital and use square brackets [ ]
For examples Plot [ ]

MATHEMATICA COMMANDS FOR Chapter 1

1. Find stationary point and then Maximum and Minimum

f[x_]:=function
Solve[f'[x]==0,x]

2. Find the y-coordinate by given x value and function

f[x_]:=function
f["Enter x value here"]

f[x_]:=(x^2)-2x+1
f[0]

3. Find the gradient of the tangent at a point

f[x_]:=function
f'["Enter x value here"]

f[x_]:=(x^2)-2x+1
f'[0]

4. Find Derivative of a function

f[x_]:=function
f'[x]//TraditionalForm

f[x_]:=Sin[x]
f'[x]//TraditionalForm

5. Composition of functions

f[x_]:=function
g[x_]:=function
f[g["Enter x value here"]]//TraditionalForm

f[x_]:=2x-1
g[x_]:=2x
f[g[x]]//TraditionalForm

6.Inverse functions

f[x_]:=function
InverseFunction[f][x]//TraditionalForm

f[x_]:=2x-1
InverseFunction[f][x]//TraditionalForm

7. To plot one graph

Plot[{"function"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{2^x},{x,0,10},PlotLegends->"Expressions"]

8. To plot Graphs of Derivative Functions

f[x_]:=function
Plot[f'[x]&&"Minimum"≤x≤"Maximum",{x,"Minimum","Maximum"},PlotRange->5]

Plot[(((x-2))^2)&&2≤x≤5,{x,0,5},PlotRange->5]

Plot[(x-2)(x-3)(x+2)&&-2≤x≤5,{x,-5,5}]

9. To plot few graphs on the same plane

Plot[{"function1","function2","function3"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotLegends->"Expressions"]

10. Solve Equations

Solve["Left side of Equation"=="Right side of Equation","solve for"]

Solve[2x==8,x]//N

11. Solve Simultaneous Equations

Solve[{equation here number one,another equation here},{variable1,variable2}]

Solve[{2x+3y==6,x-2y==4},{x,y}]//N

12. Point Gradient Form :  y-(Subscript[y, 1])=  m(x-(Subscript[x, 1]))

Solve[y-((Subscript[y, 1]))==m(x-((Subscript[x, 1]))),y]