Beyond the Basics

97. The graph of f is the graph of $y = x^{4}$ $y = x^{4}$ shifted 1 unit to the right.

Zero: $x = 1,$ $x = 1,$ multiplicity: 4
99. The graph of f is the graph of $y = x^{4}$ $y = x^{4}$ shifted 2 units up.

No zeros
101. The graph of f is the graph of $y = x^{4}$ $y = x^{4}$ shifted 1 unit to the right and reflected about the x-axis.

Zero: $x = 1,$ $x = 1,$ multiplicity: 4
103. The graph of f is the graph of $y = x^{5}$ $y = x^{5}$ shifted 1 unit up.

Zero: $x = - 1,$ $x = - 1,$ multiplicity: 1
105. The graph of f is the graph of $y = x^{5}$ $y = x^{5}$ shifted 1 unit to the left, compressed by a factor of $\frac{1}{4}$ $\frac{1}{4}$ , reflected about the x-axis, and shifted 8 units up.

Zero: $x = 1,$ $x = 1,$ multiplicity: 1
109. Maximum vertical distance: 0.25. It occurs at $x \approx 0.71 .$ $x \approx 0.71 .$
111. $f (x) = x^{2} (x + 1)$ $f (x) = x^{2} (x + 1)$
113. $f (x) = 1 - x^{4}$ $f (x) = 1 - x^{4}$
115. Degree 5 because the graph has 5 x-intercepts and 4 turning points
117. Degree 6 because the graph has 5 turning points
119. $f (x) \approx 10 x^{4}$ $f (x) \approx 10 x^{4}$ and $f (x) \approx x + 1$ $f (x) \approx x + 1$
121. $f (x) \approx x^{4} and f (x) \approx 1 - x^{2}$ $f (x) \approx x^{4} and f (x) \approx 1 - x^{2}$

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