Gateway exam practice - Math Insight

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Total points: 10

Time limit: 50 minutes

Let the variable $x$ be in the range \begin{align*} -3< x <4. \end{align*} If $y= 5 x + 1$, what is the range of the variable $y$?

$\lt y \lt$
Write the function $f(x)=33e^{ 6x+2 }$ in the form $f(x)=Ae^{kx}$. What are the values of the parameters $A$ and $k$?
$A=$
, $k=$

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Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
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Solve the equation $8 y^{4} \left(y^{2} - 10 y + 21\right) =0$ by factoring.
The solutions are $y = $

If there are more than one solution, separate answers by commas
The difference between two positive numbers is 2 and the sum of their squares is 100.
The numbers are

Separate answers by a comma.
Let $y(x) = - 7 e^{- 3 x - 8}$ and $u(x) = 7 x^{2} + x$. What is $y(u(x))$?
$y(u(x)) = $

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Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
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Find the equation for the line through the points $(6,-7)$ and $(-10,-10)$.
$y = $
Simplify the inequality below: \begin{align*} \left|2 x - 4\right|<7 \end{align*}

$\lt x \lt$
Solve for y. \begin{align*} 4 y - 8 = y + 2 \end{align*} $y = $
Compute the value of $f(f(f(8)))$ for the function $f(x)=5x+3$.
$f(f(f(8))) =$
Consider the function $f(t)=15(0.3)^t. \;\;$ Find the half-life, i.e. find $t$ such that $f(t)=\frac{1}{2}f(0).$
Half-life =

(If you round your answer, include at least 4 significant digits.)