Question 114165
Let's find values of y when x is from -3 to 3

note: remember, f(x) is the same as y





Let's evaluate {{{f(-3)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(-3)=(-3)^2+1}}} Plug in {{{x=-3}}}. In other words, replace each x with -3.



{{{f(-3)=(9)+1}}} Evaluate {{{(-3)^2}}} to get 9.



{{{f(-3)=10}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(-2)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(-2)=(-2)^2+1}}} Plug in {{{x=-2}}}. In other words, replace each x with -2.



{{{f(-2)=(4)+1}}} Evaluate {{{(-2)^2}}} to get 4.



{{{f(-2)=5}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(-1)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(-1)=(-1)^2+1}}} Plug in {{{x=-1}}}. In other words, replace each x with -1.



{{{f(-1)=(1)+1}}} Evaluate {{{(-1)^2}}} to get 1.



{{{f(-1)=2}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(0)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(0)=(0)^2+1}}} Plug in {{{x=0}}}. In other words, replace each x with 0.



{{{f(0)=(0)+1}}} Evaluate {{{(0)^2}}} to get 0.



{{{f(0)=1}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(1)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(1)=(1)^2+1}}} Plug in {{{x=1}}}. In other words, replace each x with 1.



{{{f(1)=(1)+1}}} Evaluate {{{(1)^2}}} to get 1.



{{{f(1)=2}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(2)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(2)=(2)^2+1}}} Plug in {{{x=2}}}. In other words, replace each x with 2.



{{{f(2)=(4)+1}}} Evaluate {{{(2)^2}}} to get 4.



{{{f(2)=5}}} Now combine like terms



-----------Now let's evaluate another value---------



Let's evaluate {{{f(3)}}}



{{{f(x)=x^2+1}}} Start with the given function.



{{{f(3)=(3)^2+1}}} Plug in {{{x=3}}}. In other words, replace each x with 3.



{{{f(3)=(9)+1}}} Evaluate {{{(3)^2}}} to get 9.



{{{f(3)=10}}} Now combine like terms




Now lets make a table of the values we have calculated

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> -3</TD><TD>10</TD></TR> 
<TR><TD> -2</TD><TD>5</TD></TR> 
<TR><TD> -1</TD><TD>2</TD></TR> 
<TR><TD> 0</TD><TD>1</TD></TR> 
<TR><TD> 1</TD><TD>2</TD></TR> 
<TR><TD> 2</TD><TD>5</TD></TR> 
<TR><TD> 3</TD><TD>10</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),
circle(-3,10,0.05),
circle(-3,10,0.08),
circle(-2,5,0.05),
circle(-2,5,0.08),
circle(-1,2,0.05),
circle(-1,2,0.08),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,2,0.05),
circle(1,2,0.08),
circle(2,5,0.05),
circle(2,5,0.08),
circle(3,10,0.05),
circle(3,10,0.08))}}}



Now connect the points to graph {{{y=x^2+1}}}  (note: the more points you plot, the easier it is to draw the graph)

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, x^2+1),
circle(-3,10,0.05),
circle(-3,10,0.08),
circle(-2,5,0.05),
circle(-2,5,0.08),
circle(-1,2,0.05),
circle(-1,2,0.08),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,2,0.05),
circle(1,2,0.08),
circle(2,5,0.05),
circle(2,5,0.08),
circle(3,10,0.05),
circle(3,10,0.08))}}}