Ex1: review exercises - functions

These exercises are taken from: Calculus Volume 1 from OpenStax, Print ISBN 193816802X, Digital ISBN 1947172131, https://www.openstax.org/details/calculus-volume-1

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E1. Evaluate the function \(f(x) = 4x^2 + 3x +1\) for a. \(f(-3)\), b. \(f(a)\), c. \(f(a + h)\).

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E2. Scatch the plot of the following function \(f(x) = 2x^3 + 1\).

(Hint: Start from a table evaluating the function at several points and then put these into a graph.)

Is this an increasing or a decreasing function?

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E3. For the pair of functoins \(f(x) = x^2 - 2\) and \(g(x) = 2x + 4\) find and simplify a. \(f - g\), b. \(f \times g\), c. \(g \circ f\).

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E4. Decompose the following function into 2 simpler functions \(f(x) = \log(x^2 + 4/x)\)

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E5. Find the slope of the line passing through these points: \((-1, 4)\) and \((3, -1)\).

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E6. Write the slope-intercept form and the standard form of the line that has slope 3 and passes through the point \((-3, 2)\).

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E7. Scatch the plot of the line \(2x + 3y = 6\).

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E8. For the function in the graph, indicate all its local and global extrama (minima and maxima).

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E9. Find the average rate of growth of the function in the graph in the intervals \(x \in (0, 2)\), \(x \in (2, 4)\) and \(x \in (0, 4)\).

Scatch into the graph lines with the same slopes.

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E9.