Consider the following function. f(x)=√x-1, (17,4) (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. 10- -5 y y 10 8 6 10 8- 6- X 0 5 5 10 X 10 X 15 15 20 20 X y 8 y 6 10 8 6 2 5 5 10 X 10 X 15 15 20 20
Consider the following function. f(x)=√x-1, (17,4) (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. 10- -5 y y 10 8 6 10 8- 6- X 0 5 5 10 X 10 X 15 15 20 20 X y 8 y 6 10 8 6 2 5 5 10 X 10 X 15 15 20 20
Chapter3: Functions
Section3.5: Transformation Of Functions
Problem 5SE: How can you determine whether a function is odd or even from the formula of the function?
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![### Understanding Tangent Lines
#### Consider the following function:
\[ f(x) = \sqrt{x} - 1, \quad (17, 4) \]
##### (a) Find an equation of the tangent line to the graph of \( f \) at the given point.
\[ y = \]
The correct answer was not provided.
#### (b) Use a graphing utility to graph the function and its tangent line at the point.
There are four graphs displayed. The objective is to identify the correct one that shows the function \( f(x) = \sqrt{x} - 1 \) along with its tangent line at the point (17, 4).
1. **First Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, closely aligned with the curve around the point (17, 4).
2. **Second Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, not closely aligned with the curve around the point (17, 4).
3. **Third Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, not closely aligned with the curve around the point (17, 4).
4. **Fourth Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, with an incorrect alignment.
- The answer indicates that this graph is incorrect.
The correct graph should show that the tangent line at the point (17, 4) aligns with the curve of the function \( f(x) = \sqrt{x} - 1 \) at that point. The first graph](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc6cf166-7954-4fc5-a62e-be3094a9be9e%2F577a1359-fa85-4eaf-a12a-93dc41b734b2%2Fi5eykm_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Tangent Lines
#### Consider the following function:
\[ f(x) = \sqrt{x} - 1, \quad (17, 4) \]
##### (a) Find an equation of the tangent line to the graph of \( f \) at the given point.
\[ y = \]
The correct answer was not provided.
#### (b) Use a graphing utility to graph the function and its tangent line at the point.
There are four graphs displayed. The objective is to identify the correct one that shows the function \( f(x) = \sqrt{x} - 1 \) along with its tangent line at the point (17, 4).
1. **First Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, closely aligned with the curve around the point (17, 4).
2. **Second Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, not closely aligned with the curve around the point (17, 4).
3. **Third Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, not closely aligned with the curve around the point (17, 4).
4. **Fourth Graph:**
- Axes: The vertical axis (y) ranges from 0 to 10, and the horizontal axis (x) ranges from -5 to 20.
- Plot: The function is plotted in red.
- Additional Line: Tangent line drawn in red, with an incorrect alignment.
- The answer indicates that this graph is incorrect.
The correct graph should show that the tangent line at the point (17, 4) aligns with the curve of the function \( f(x) = \sqrt{x} - 1 \) at that point. The first graph
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