Practice Test 44 - Algebra 1

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

Translate the recursive definition $a_1=7$ and $a_{n+1}=a_n-2$ into an explicit formula for $a_n$ .
Given $P(x)=(x+1)^3(x-2),$ use the zeros and multiplicities to sketch a rough graph. Which statement best describes the behavior at each zero?
Find the intersection point(s) of the line and the parabola by solving the system: $\begin{cases} y = 2x + 1 \\ y = x^2 + 1 \end{cases}$ Give all solutions $(x,y)$ .
Order the following functions by growth rate for large $x$ (from slowest to fastest): $ f(x)=5x$ (linear), $g(x)=10x^2$ (quadratic), $p(x)=x^4$ (polynomial), $h(x)=1.2^x$ (exponential).
For the function $f(x)=\frac{1}{2}x+6$ , find the average rate of change of $f(x)$ from $x=-2$ to $x=4$ .
Why is $5+\sqrt{3}$ irrational? Choose the best reasoning.
The arithmetic sequence $-2,\ 1,\ 4,\ 7,\ldots$ can be represented by a linear function where $x$ is the term number and $f(x)$ is the value of the term. If $f(1)=-2$ , what is $f(x)$ ?
Translate the explicit formula $a_n = 5\cdot\left(\tfrac{1}{2}\right)^{n-1}$ into a recursive definition.
A car's value is modeled by $V(t)=20000(1+r)^t$ and it depreciates 15% each year. Which function correctly models this situation?
Express $\sqrt{x}$ using a rational exponent.
If $p(x) = x^2 - 4x + 1$ and $p(m) = p(n)$ where $m \neq n$ , what is the relationship between $m$ and $n$ ?
If $f(x) = x^2 - 3x + 2$ and $g(x) = x + 1$ , which statement about the polynomial $h(x) = f(x) \cdot g(x)$ is correct?
The graph shows temperature $T$ as a function of time $t$ during a chemical reaction. Based on the graph and the context, which domain restriction is most justified?
The graph of $x^2 + y^2 = 25$ is a circle. If a student randomly selects the point $(3, -4)$ , what can be concluded about this point's relationship to the equation?
An economist models profit using $P = 200(q + 5)^2 - 50(q + 5) - 1000$ , where $q$ represents quantity produced. To understand how profit depends on the shifted quantity $(q + 5)$ , which analysis is most revealing?
For $f(x)=2x^2+1$ , what is the average rate of change of $f(x)$ from $x=1$ to $x=3$ ? Use $\frac{f(b)-f(a)}{b-a}$ . (Compare the points $(1,f(1))$ and $(3,f(3))$ .)
Complete the square to rewrite $f(x)=x^2-6x+2$ in vertex form, then identify the vertex and axis of symmetry.
Consider the quadratic function $f(x) = -2x^2 + 8x - 6$ . Which point represents the vertex of this function's graph?
Function $c$ is described as: "A quadratic function with vertex at $(2, -1)$ that opens upward and passes through the point $(0, 3)$ ." The graph shows function $d(x)$ . Which statement about their y-intercepts and vertices is correct?
If $g(x) = 3x - 2$ and $g(a) = 10$ , what is the value of $g(a + 1)$ ?

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