Practice Test 9 - Algebra 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

A taxi charges a base fee of $4 plus $2.50 per mile. Let $C$ be the total cost (in dollars) and let $m$ be the number of miles ridden. What equation represents the relationship between $C$ and $m$ ?
A student says: "Fractional exponents are just a convenient notation; they don't have to match exponent rules." Which response best reflects the mathematical reasoning used to define rational exponents (assume $b>0$ )?
A gym membership costs $35 to sign up plus $18 per month. What is the formula for the total cost $C(m)$ (in dollars) after $m$ months?
Which function represents exponential decay?
Is point $(2,1)$ in the solution region of the inequality $y < x - 2$ ?
Two sequences are given: Sequence X has the explicit formula $x_n = 15 - 2n$ and Sequence Y is defined recursively as $y_1 = 13$ and $y_n = y_{n-1} - 2$ . How do these sequences compare?
See $x^4-81$ as $(x^2)^2-9^2$ (a difference of squares) and factor completely.
A city's population grows according to $P(t) = 50000 \cdot 1.12^t$ where $t$ is in years. To model monthly population changes, which expression is equivalent and shows the monthly growth factor?
Complete the square to find the vertex of the quadratic function $f(x)=x^2+8x+3$ .
The expression $3(x + 2)^2 - 5(x + 2) + 7$ can be analyzed by viewing certain parts as single entities. If we let $u = x + 2$ , which of the following best describes the structure of the resulting expression?
A bakery uses $P(n)=\frac{60}{n}$ to estimate the time (in minutes) it takes to package $n$ identical gift boxes when $n$ workers are packaging, where $n$ is the number of workers. The formula works mathematically for many values of $n$ , but not all values make sense in context. Which is the most appropriate realistic domain for $P(n)$ ?
A gym charges a monthly membership fee plus a one-time sign-up fee. The total cost $C$ (in dollars) after $m$ months is modeled by $C = 35m + 60$ . What does the 60 represent in this context?
Which expression is equivalent to $\sqrt{x^3}$ ? (Write in rational exponent form.)
A theater has 200 seats. The function $R(n)=15n$ gives the revenue (in dollars) from selling $n$ tickets, where $n$ is the number of attendees. What domain makes sense for $n$ in this context?
Use the table to evaluate $f(g(2))$ . Table for $g$ : - $g(2)=5$ Table for $f$ : - $f(5)=12$
The value of a laptop after $t$ years is modeled by $V(t)=25000(0.88)^t$ . Is this exponential growth, exponential decay, or neither?
A projectile's height $h$ (in feet) above the ground after $t$ seconds is modeled by $h = -16t^2 + 64t + 80$ . If the projectile hits the ground when $h = 0$ , which method would be most efficient for finding when this occurs?
Interpret the expression $f(x)=\left(x^2+1\right)^3$ as an operation on parts. What are the main parts of the composition?
What is the starting point of $f(x)=\sqrt{x+1}$ ?
Graph the inequality $2x + y > 4$ . Which boundary line and shading are correct?

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