To determine: a) To graph: The function f(x)=x2+1 in the region x≤0 b) Whether the function f(x)=x2+1 in the region x≤0 is a one-to-one function with the help of graphical representations.

Question

To determine:  a) To graph: The function f(x)=x2+1 in the region x≤0  b) Whether the function f(x)=x2+1 in the region x≤0 is a one-to-one function with the help of graphical representations.

Kaylen Campos · Accepted Answer

Step 1 Use the transformation of the graph of the parent function y=x2 to graph the given function f(x)=x2+1 The graph of y=x2 forms a parabolic curve. As per the properties of the transformation of the graph, the graph of the function f(x)=x2+1 is the graph of the parent function y=x2, which is shifted to 1 unit upwards in the +y direction. Now, consider the given function, f(x)=x2+1 To graph the given function f(x) , take some random values of x∈R{ 9domain set and calculate f(x) for those values. The results are the coordinates of points in the x-y plane Thus, the table that shows the coordinate points for the graph of the function f(x)=x2+1 is, xf(x)=x2+101−12−25−310 Refer to the table above. Plot the points on the graph by following the properties of transformation of graph. Draw the graph of the function f(x)=x2+1, x≤0  The graph of the function f(x)=x2+1 is parabolic and is defined in the region x≤0

meldElafellrbo · Accepted Answer

Step 1  Consider the function n=f(x)  If no horizontal line intersects the graph from the given function in more than one point, then the function is one-to-one function.  Now, consider the graph of the given function f(x)=x2+1, x≤0. Draw horizontal lines in the graph:    The horizontal lines intersect the graph at only one point on the curve individually.  So, the relation given in the graph represents a one-to-one function.

To determine: a) To graph: The function f(x)=x^{2}+1 in the region

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