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The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 1) f(x)=√x+3 +

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 1) f(x)=√x+3 +

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The graph of a one-to-one function \( f \) is given. Draw the graph of the inverse function \( f^{-1} \) as a dashed line or curve. 1) \( f(x) = \sqrt{x} + 3 \) *Graph Explanation*: The graph shows a square root function, which starts at the point \((0, 3)\) and curves upward to the right. The x-axis and y-axis are clearly marked with intervals of 1, ranging from -5 to 5 on both axes. --- The graph of an exponential function is given. Match the graph to one of the following functions. Circle the letter of your answer. 6) A) \( f(x) = 4^x \) B) \( f(x) = 4^x - 1 \) C) \( f(x) = 4^x + 1 \) D) \( f(x) = \frac{4^x + 1}{4} \) *Graph Explanation*: The graph depicts an exponential function that increases rapidly. It moves from the lower left near (-2, -4) and rises steeply to the right, passing just above the point (0, 0) and continuing upwards. The axes are marked similarly with intervals of 1. --- Solve the equation. 7) \( 18^x = 1 \) \( x = \underline{\hspace{6cm}} \) 8) \( 2^{-x} = \frac{1}{16} \) \( x = \underline{\hspace{6cm}} \)
Transcribed Image Text:The graph of a one-to-one function \( f \) is given. Draw the graph of the inverse function \( f^{-1} \) as a dashed line or curve. 1) \( f(x) = \sqrt{x} + 3 \) *Graph Explanation*: The graph shows a square root function, which starts at the point \((0, 3)\) and curves upward to the right. The x-axis and y-axis are clearly marked with intervals of 1, ranging from -5 to 5 on both axes. --- The graph of an exponential function is given. Match the graph to one of the following functions. Circle the letter of your answer. 6) A) \( f(x) = 4^x \) B) \( f(x) = 4^x - 1 \) C) \( f(x) = 4^x + 1 \) D) \( f(x) = \frac{4^x + 1}{4} \) *Graph Explanation*: The graph depicts an exponential function that increases rapidly. It moves from the lower left near (-2, -4) and rises steeply to the right, passing just above the point (0, 0) and continuing upwards. The axes are marked similarly with intervals of 1. --- Solve the equation. 7) \( 18^x = 1 \) \( x = \underline{\hspace{6cm}} \) 8) \( 2^{-x} = \frac{1}{16} \) \( x = \underline{\hspace{6cm}} \)
**Exponential and Logarithmic Expressions** **Problem 9:** Solve for \( x \) in the equation: \[ 5^x = 125 \] \[ x = \underline{\hspace{2cm}} \] **Problem 10:** Solve for \( x \) in the equation: \[ \left(\frac{1}{7}\right)^x = 49 \] \[ x = \underline{\hspace{2cm}} \] **Solve the equation:** **Problem 11:** \[ 27^{4x + 5} = 243^{4x} \] \[ x = \underline{\hspace{9cm}} \] **Change the exponential expression to an equivalent expression involving a logarithm.** **Problem 12:** \[ M^2 = x \] \[ \text{Answer} \:\: \underline{\hspace{9cm}} \] **Change the logarithmic expression to an equivalent expression involving an exponent.** **Problem 13:** \[ \log_b K = 5 \] \[ \text{Answer} \:\: \underline{\hspace{9cm}} \]
Transcribed Image Text:**Exponential and Logarithmic Expressions** **Problem 9:** Solve for \( x \) in the equation: \[ 5^x = 125 \] \[ x = \underline{\hspace{2cm}} \] **Problem 10:** Solve for \( x \) in the equation: \[ \left(\frac{1}{7}\right)^x = 49 \] \[ x = \underline{\hspace{2cm}} \] **Solve the equation:** **Problem 11:** \[ 27^{4x + 5} = 243^{4x} \] \[ x = \underline{\hspace{9cm}} \] **Change the exponential expression to an equivalent expression involving a logarithm.** **Problem 12:** \[ M^2 = x \] \[ \text{Answer} \:\: \underline{\hspace{9cm}} \] **Change the logarithmic expression to an equivalent expression involving an exponent.** **Problem 13:** \[ \log_b K = 5 \] \[ \text{Answer} \:\: \underline{\hspace{9cm}} \]
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