Recent questions in Precalculus

Transformations of functions

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. $$\displaystyle{g{{\left({x}\right)}}}=\sqrt{\frac{1}{4}}{x}$$

Probability and combinatorics

Matrices

For each topic, decide how a scatterplot of the data would likely look. Explain your reasoning. Speed of a runner and amount of time to complete a race

Probability and combinatorics

$$\displaystyle{\left(-{3}{j}^{{-{{5}}}}\cdot{k}^{{6}}\right)}^{{4}}$$

Probability and combinatorics

$$\displaystyle{\left({3}{t}^{{2}}−{4}{s}\right)}^{{2}}$$

Transformations of functions

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. $$g(x) = 3 - ||x||$$

Composite functions

Matrices

Matrices

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ \hline f(x) & 2.4 & 2.88 & 3.456 & 4.147 & 4.977 & 5.972 & 7.166 & 8.6 & 10.32 & 12.383 \ \hline \end{array}

Composite functions

Find derivatives of the functions defined as follows. $$\displaystyle{y}={3}\dot{{\lbrace}}{4}^{{{x}^{{{2}}}+{2}}}$$

Probability and combinatorics

Pure acid is to be added to a $$20\%$$ acid solution to obtain 28 L of a $$40\%$$ acid solution. What amounts of each should be used?

Probability and combinatorics

$$\displaystyle{\left(−{2}{v}^{{2}}\right)}{\left({3}{v}\right)}{\left({5}{v}^{{5}}\right)}$$

Probability and combinatorics

Sleep: Mean 7.35 and Range $$5.5-8.8$$ Light physical activity: Mean 8.71 and Range $$3.0-16.0$$ Moderate physical activity: Mean 3.36 and Range $$0.71-8.3$$ Hard physical activity: Mean 0.78 and Range $$0-4.1$$ Very hard physical activity: Mean 0.14 and Range $$0-1.05$$ On the average. how many hours per day did the women sleep?

Composite functions

Find derivatives of the functions defined as follows. $$\displaystyle{f{{\left({z}\right)}}}={\left({2}{z}+{e}^{{-{z}^{{{2}}}}}\right)}^{{{2}}}$$

Transformations of functions

Matrices

Matrices

Vectors

v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: $$(a, b) + (c, d) = (a + c, b + d) k (a, b) = (kb, ka)$$ (attention in this part) show that V is not linear space.

Probability and combinatorics