# Consider the vector-valued function r\left(t\right)=3t^2i+\left(t-1

Consider the vector-valued function $$\displaystyle{r}{\left({t}\right)}={3}{t}^{{2}}{i}+{\left({t}-{1}\right)}{j}+{t}{k}$$. Write a vector-valued function u(t) that is the specified transformation of r. A horizontal tra
ation one unit in the direction of the positive x-axis

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Sue Leahy
Step 1
The given function is $$\displaystyle{r}{\left({t}\right)}={3}{t}^{{2}}{i}+{\left({t}-{1}\right)}{j}+{t}{k}$$
Step 2
Here $$\displaystyle{x}{\left({t}\right)}={3}{t}^{{2}},{y}{\left({t}\right)}={t}-{1},{z}{\left({t}\right)}={t}$$
A horizontal tra
ation one unit in the direction of the positive x-axis gives the function x(t) as,
$$\displaystyle{x}{\left({t}\right)}={3}{t}^{{2}}+{1}$$
Thus, $$\displaystyle{r}{\left({t}\right)}={\left({3}{t}^{{2}}+{1}\right)}{i}+{\left({t}-{1}\right)}{j}+{t}{k}$$.