Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
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
The point $(-9, 1)$ lies on the graph of $f(x)$. Given the transformation $g(x) = 2f(-x) + 3$, we ne...
FunctionsTransformationsGraphing
2025/6/12
The problem asks us to find the function notation and equation form of a transformed absolute value ...
FunctionsTransformationsAbsolute ValueFunction NotationVertical StretchVertical ShiftHorizontal Shift
2025/6/12
The problem requires us to express the transformed function $g(x)$ in both function notation and equ...
Function TransformationsVertical ShiftsHorizontal ShiftsFunction NotationEquation FormPolynomial FunctionsSquare Root Functions
2025/6/12
The point $(1, -12)$ is on the graph of $f(x)$. Given the transformation $g(x) = \frac{1}{3}f(x+6) -...
Function TransformationsGraphingHorizontal ShiftVertical ShiftVertical Compression
2025/6/12
The problem asks us to draw the graph of $g(x) = f(x) - 4$ in the first coordinate grid and $g(x) = ...
Graph TransformationsFunctionsVertical ShiftHorizontal Shift
2025/6/12
We are given that the point $(8, -5)$ lies on the graph of $f(x)$. We are also given the transformat...
FunctionsTransformations of FunctionsGraphing
2025/6/12
We are given the transformed function $f(x) = \frac{1}{8}h(x-6)-5$ and we want to determine the tran...
Function TransformationsVertical CompressionVertical ShiftHorizontal Shift
2025/6/12
The problem asks to identify the transformations applied to the parent function $h(x)$ to obtain the...
Function TransformationsTransformations of GraphsReflectionVertical StretchVertical Shift
2025/6/12
The problem asks to identify the type of transformation applied to the parent function $g(x)$ to obt...
Function TransformationsVertical ShiftsFunction Analysis
2025/6/12