Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Table 1.2.3, and then applying the appropriate transformations.

9. \(y = {\bf{1}} + {x^{\bf{2}}}\)

Short answer

The graph of function \(y = 1 + {x^2}\) is obtained from the graph of \(y = {x^2}\) by shifting the graph by 1 unit upward.

Step-by-step solution

Write the transformation to find the graph of \(y = {\bf{1}} + {x^{\bf{2}}}\)

The graph of function \(y = 1 + {x^2}\) is obtained from the graph of \(y = {x^2}\) by shifting the graph by 1 unit upward.

Sketch the graph of transformation from \(y = {x^{\bf{2}}}\) to \(y = {\bf{1}} + {x^{\bf{2}}}\)

The figure below represents the graph of \(y = {x^2}\) as shown below:

The sketch below represents the graph of \(y = 1 + {x^2}\):

Thus, the graph of the function \(y = 1 + {x^2}\) is obtained.