Questions: Work Exercises 97 to 101 in order. A. Shrink the graph horizontally by a factor of y. B. Shift 9 units to the left. C. Shift 9 units to the right. D. Shift the graph 9 units upward. E. Reflect the graph across the y-axis. F. Shrink the graph vertically by a factor of 9. G. Shift the graph 9 units downward. H. Reflect the graph across the x-axis. 98. Graph Y1=4^X and Y2=-4^X+9 in the window [-5,5] by [-10,10] to support the answer in Exercise 97. 99. Use a calculator to find an approximation for the zero of the function Y2 in Exercise 98. Zero of the function Y2 is approximately 1.5849625. (Simplify your answer. Type an integer or decimal rounded to seven decimal places as needed.) 100. Solve -4^x+9=0 for x, expressing x in terms of a base 4 logarithm. x=

Work Exercises 97 to 101 in order.
A. Shrink the graph horizontally by a factor of y.
B. Shift 9 units to the left.
C. Shift 9 units to the right.
D. Shift the graph 9 units upward.
E. Reflect the graph across the y-axis.
F. Shrink the graph vertically by a factor of 9.
G. Shift the graph 9 units downward.
H. Reflect the graph across the x-axis.
98. Graph Y1=4^X and Y2=-4^X+9 in the window [-5,5] by [-10,10] to support the answer in Exercise 97.

99. Use a calculator to find an approximation for the zero of the function Y2 in Exercise 98.

Zero of the function Y2 is approximately 1.5849625.
(Simplify your answer. Type an integer or decimal rounded to seven decimal places as needed.)
100. Solve -4^x+9=0 for x, expressing x in terms of a base 4 logarithm.

x=
Transcript text: Work Exercises 97 to 101 in order. $\sqcup$ A. Shrink the graph horizontally by a tactor of $y$. B. Shift 9 units to the left. C. Shift 9 units to the right. D. Shift the graph 9 units upward. E. Reflect the graph across the $y$-axis. F. Shrink the graph vertically by a factor of 9 . G. Shift the graph 9 units downward. H. Reflect the graph across the $x$-axis. 98. Graph $Y_{1}=4^{X}$ and $Y_{2}=-4^{X}+9$ in the window $[-5,5]$ by $[-10,10]$ to support the answer in Exercise 97. A. B. c. D. 99. Use a calculator to find an approximation for the zero of the function $Y_{2}$ in Exercise 98. Zero of the function $\mathrm{Y}_{2}$ is approximately 1.5849625 . (Simplify your answer. Type an integer or decimal rounded to seven decimal places as needed.) 100. Solve $-4^{x}+9=0$ for $x$, expressing $x$ in terms of a base 4 logarithm. \[ x=\square \] Clear all
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Solution

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Solution Steps

Step 1: Identify the transformation in Exercise 97
  • The problem asks to identify the transformation applied to the graph.
  • The correct answer is D: Shift the graph 9 units upward.
Step 2: Graph the functions in Exercise 98
  • Graph \( Y_1 = 4^X \) and \( Y_2 = -4^X + 9 \) in the window \([-5, 5]\) by \([-10, 10]\).
  • The correct graph is D, which shows the transformation of \( Y_1 \) shifted 9 units upward to form \( Y_2 \).
Step 3: Find the zero of the function \( Y_2 \) in Exercise 99
  • Use a calculator to find the zero of the function \( Y_2 = -4^X + 9 \).
  • The zero of the function \( Y_2 \) is approximately \( 1.5849625 \).

Final Answer

  1. The transformation is shifting the graph 9 units upward.
  2. The correct graph is D.
  3. The zero of the function \( Y_2 \) is approximately \( 1.5849625 \).
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