Master Algebra 1 Word Problems with our Comprehensive Practice

show that the following sequence converge
${\displaystyle a_n=5+\frac{1}{n}}$

Make the first 10 terms of the sequence. Logs are to base 2.
Indicate whether the sequence is increasing, decreasing, non-increasing, or non-decreasing. The sequence may have more than one of those properties.
The ${\displaystyle n^{th}}$ term is ${\displaystyle \lceil \log \rceil }$

Prove that sequence is Cauchy. Use defenition only
${\left\{\frac{n}{n+1}\right\}}_{n=1}^{\mathrm{\infty }}$

Graph the following quadratic function ${\displaystyle f\left(x\right)=x^2-4x-1}$

Solve the inequality:
${\displaystyle 5x^2-3x>8}$

Simplify the following expression:
${\displaystyle \frac{2}{y+3}-\frac{1}{y^2+7y+12}}$

Find y, if
${\displaystyle 2{\cos }^2\left(y\right)-\cos \left(y\right)-1=0}$

${\displaystyle 10x^2-40=0}$

Find the coordinats if:
${\displaystyle y=x^2+3x}$
and
y=4x+6

Show that the function is a linear transformation. Is it also an isomoporphism?
T(f(t))=t(f'(t)) from ${\displaystyle P_2\to P_2}$

Use the ptoperties of logarithms to expand the following expression ${\displaystyle \log \left(\frac{z^3}{\sqrt{x^{5}y}}\right)}$

Consider the funstion (x)=${\displaystyle \sqrt{x-1}+10}$ for the domain ${\displaystyle [1,\mathrm{\infty })}$
Find ${\displaystyle f^{-1}\left(x\right)}$, where ${\displaystyle f^{-1}}$ is the inverse of f.
Also state the domain of ${\displaystyle f^{-1}}$ in interval notation

y=-7x-10
Is y defined as a function of x by the equation?

The function ${\displaystyle A=7.7{\left(0.92\right)}^t}$ represents an exponential growth or decay function.
A.
Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?
a.
Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92
b.
Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08
c.
Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08
d.
. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92
e.
None of these

Is the following equation a function ${\displaystyle f\left(x\right)=5x+7?}$ Why?

Use the tangent line to approximate f(4.01), given that f(4)=5 and f'(4)=7

Tell whether the function is linear, an absolute value function, a quadratic function, another polynomial function or rational one.
${\displaystyle p\left(x\right)=x^2+x–10.}$

Classify each following function:
a) ${\displaystyle f\left(x\right)=\log 7\left(x\right)}$
b) ${\displaystyle g\left(x\right)=\sqrt[7]{x}}$
c) ${\displaystyle h\left(x\right)=\frac{2x^3}{7–x^2}}$
d) ${\displaystyle u\left(t\right)=1–1.1t_{2.57}{t}^2}$
e) $v(t)=7^t$
f) $w(\theta )=\sin \theta {\cos }^7\theta$

Given:
A parallelogram ${\displaystyle XYZW,\overline{YZ}=2b,\overline{ZW}=a+2,\overline{WX}=b+1,\overline{XY}=3a-4}$

Evaluate the given expression and write an answer without exponents:${\displaystyle {(-1)}^4+2{(-3)}^4}$