Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem gives the formula $s = \frac{a}{1-r}$. We are asked to (i) find the value of $s$ when $a...
Formula ManipulationSubstitutionSolving Equations
2025/6/13
We are given the formula $s = \frac{a}{1-r}$ and are asked to find the value of $s$ when $a = 81$ an...
EquationsSubstitutionFractions
2025/6/13
Find two positive numbers whose sum is 110 and whose product is maximized.
OptimizationQuadratic FunctionsCalculus (Implicitly)MaximizationWord Problem
2025/6/12
The problem requires us to analyze the transformation of a parabola from its parent function $f(x) =...
Quadratic FunctionsTransformationsDomainRangeFunction Notation
2025/6/12
We are given three functions: $f(x) = \frac{1}{5}x^2$, $p(x) = -x$, and $z(x) = x + 8$. We need to f...
Function CompositionTransformationsQuadratic FunctionsVertical CompressionVertical Shift
2025/6/12
We are given the graph of a parabola $g(x)$ which is a transformation of the parent function $f(x) =...
Quadratic FunctionsTransformations of FunctionsVertex FormDomain and RangeParabolas
2025/6/12
We are given three functions: $f(x) = -\frac{1}{2}x^2$, $z(x) = x - 4$, and $p(x) = x + 5$. First, w...
Function CompositionTransformations of FunctionsQuadratic FunctionsVertical CompressionHorizontal ShiftReflection
2025/6/12
The problem describes a transformation of the parent function $f(x) = |x|$ to a transformed function...
Function TransformationsAbsolute Value FunctionsDomain and RangeGraphing
2025/6/12
We are given three functions: $f(x) = \frac{1}{x}$, $r(x) = x+4$, and $m(x) = 8x$. We need to find t...
FunctionsComposite FunctionsTransformationsVertical StretchHorizontal Shift
2025/6/12
Given the point $(2, 5)$ on the graph of $f(x)$, we want to find a point on the graph of $y = f(x - ...
Function TransformationsGraphingHorizontal ShiftVertical Shift
2025/6/12