Substitution

Our substitution feature allows you to answer the question "What would be the value of this expression if we substituted a different value for A?," without ever changing the original value of A.

Using the ‘with’ substitution function, you can replace a variable in an expression with a constant value, another variable expression, or a list.

You can find this function in the “Advanced” section of the “Functions” menu on the keypad, or ‘with’ can also be typed directly into an expression line using your keyboard.

 

Substitution within a Function

Where would the parabola \(f\left(x\right)=ax^{2}+bx+c\) move if \(b\) were \(-1\)? Model \(f\left(x\right)\) after substituting \(b\) with \(-1\) to visualize the change.

Image of graphing calculator Graphs of two parabolas.  The first is modeled when b=1 and the second is modeled when b = -1.

Next, trying graphing the vertex of the original function \((V)\) and using substitution to also graph the vertex when \(b = -1\).

Graphs of two parabolas and their vertices.  The first is modeled when b=1 and the second is modeled when b = -1

 

Substitution with a List

How do changes to \(a\), \(b\), and \(c\) affect the path of the vertex of the parabola? By substituting \(b\) with a list, you can model the path that the vertex would take.

First, graph the vertex of the original function \((V)\). Then, try substituting \(b\) with a list of possible values.

You try! Open the graph below and try it out. Use the sliders to change the values of \(a\), \(b\), and \(c\) and see how they compare to the path graphed in line 6. Example Graph.

Note: You can learn more about lists in our Help Center.

Animation of adding V with b = [-5,...5] to the graph and using the slider for b to follow the path of the vertex.

 

Substitution within the Same Expression Line

The first expression line shows the value of m divided by n plus m when m equals 10 and n equals 2.  The second shows the value of a divided by 10 when a equals 2 times b and b is defined in a third line as equal to -5.

You can evaluate expressions by substituting variables with constant values in the same line. You can also substitute a variable with another expression, but if that expression depends on a free variable, it will need to be defined separately.

Points plotted along the function y=sin(x) when x is between 0 and 2pi.

By substituting the variable \(L\) with a list of values, you can quickly plot points along the function \(y=sin(x)\)

 

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