Questions: 1) For the linear function f(x) = 2x - 3, find each of the following: a. f'(x) = b. Create a table of values for f(x) and f'(x). Graph both f(x) and f'(x) Make sure the graph is appropriately labeled.

1) For the linear function f(x) = 2x - 3, find each of the following:
a. f'(x) =
b. Create a table of values for f(x) and f'(x).

Graph both f(x) and f'(x)
Make sure the graph is appropriately labeled.

Transcript text: 1) For the linear function $f(x)=2 x-3$, find each of the following: a. $f^{\prime}(x)=$ b. Create a table of values for $f(x)$ and $f^{\prime}(x)$. Graph both $f(x)$ and $f^{\prime}(x)$ Make sure the graph is appropriately labeled.

Solution

Solution Steps

Step 1: Find the derivative of the function

The given function is $ f(x) = 2x - 3 $.

To find the derivative, we use the power rule:

\[ f^{\prime}(x) = \frac{d}{dx}(2x - 3) = 2 \]

Step 2: Create a table of values for $ f(x) $ and $ f^{\prime}(x) $

Let's choose some values for $ x $ and calculate $ f(x) $ and $ f^{\prime}(x) $.

| $ x $ | $ f(x) = 2x - 3 $ | $ f^{\prime}(x) = 2 $ | |---------|---------------------|-------------------------| | -2 | -7 | 2 | | -1 | -5 | 2 | | 0 | -3 | 2 | | 1 | -1 | 2 | | 2 | 1 | 2 |

Final Answer

The derivative of the function is $ f^{\prime}(x) = 2 $.
The table of values is provided above.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -8, "ymax": 2}, "commands": ["y = 2x - 3", "y = 2"], "latex_expressions": ["$f(x) = 2x - 3$", "$f^{\\prime}(x) = 2$"]}

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