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How do you graph the function #y=f(x)=x^2+1#?

Answer 1

Eva Abramson

See answer below

Given: #f(x) = x^2 + 1#

You can use point plotting. Select any #x# value and then calculate the #y# value and plot.

#ul(" "x" "| " "y" ")# #""-4" "|" "17# #""-2" "|" "5# #" "0" "|" "1# #" "2" "|" "5# #" "4" "|" "17#

or you can realize that #x^2 + 1# is a vertical shift up #1# of the parent function #f(x) = x^2#

or you can just graph the function using a graphing calculator.

TI-83, 84: Y= X^2 + 1 then select GRAPH

graph{x^2+1 [-5, 5, -4, 20]}

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Answer 2

Kennedy Adams

To graph the function ( f(x) = x^2 + 1 ), you can plot points by selecting values for ( x ) and then evaluating ( f(x) ) to find corresponding ( y ) values. Another method is to recognize that the graph of ( y = x^2 ) is a parabola with its vertex at the origin, and adding 1 shifts the entire graph upwards by one unit. So, the vertex of ( y = f(x) ) is at the point (0, 1). From there, you can use the symmetry of the parabola to plot additional points or sketch the curve accordingly.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.