Find an equation of y as a function of x for the parametric equations given below by eliminating the parameter. Also, indicate the direction of the curve. $$x = t + 1 , \quad y = e ^ { t } , \quad t \in ( - \infty , \infty )$$
A) $y = e ^ { x + 1 } , x \in ( - \infty , \infty ) \text {, left to right }$
B) $y = e ^ { x - 1 } , x \in ( - \infty , \infty ) \text {, left to right }$
C) $y = e ^ { x + 1 } , x \in ( - \infty , \infty ) \text {, right to left }$
D) $y = e ^ { x - 1 } , x \in ( - \infty , \infty ) \text {, right to left }$

Question

Quizplus · Accepted Answer

To eliminate the parameter $t$, we solve the first equation for $t$: $t = x - 1$. Substituting this into the second equation gives $y = e^{x-1}$. The direction is left to right because as $t$ increases, $x$ increases.

Find an Equation of Y as a Function of X x=t+1,y=et,t∈(−∞,∞)x = t + 1 , \quad y = e ^ { t } , \quad t \in ( - \infty , \infty )x=t+1,y=et,t∈(−∞,∞)

Find an Equation of Y as a Function of X $x = t + 1 , \quad y = e ^ { t } , \quad t \in ( - \infty , \infty )$