🧮 algebra

1. **Problem Statement:** We need to determine which polynomial matches the graph described. The graph has:

1. **State the problem:** We have the function $y=2^x$ (solid line) and a dilation from the y-axis by a factor $a$ (dotted line). We need to determine if $a$ is greater than 1, les

1. The problem asks whether the dilation factor $a$ from the x-axis applied to the graph $y=2^x$ is greater than or less than 1. 2. A dilation from the x-axis by a factor $a$ means

1. **State the problem:** Solve the inequality $2x - 3 > 1$. 2. **Write the inequality:**

1. **Problem:** Determine the domain and range of the function shown in the first graph, which is a line segment from $(-3,-3)$ (not included) to $(1,4)$ (included). 2. **Formula a

1. The problem is to find the internal ratio of the parts 2 : 3 : 5. 2. The internal ratio means dividing a whole into parts proportional to 2, 3, and 5.

1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and need to understand its behavior. 2. **Formula and rules:** The function involves an absolute value, which

1. The problem asks for the domain and range of a function, but the function itself is not specified. 2. The domain of a function is the set of all possible input values (x-values)

1. The problem is to find the domain and range of a function. 2. The domain of a function is the set of all possible input values (x-values) for which the function is defined.

1. **State the problem:** We are given the function $$h(x) = -4|x - 5|$$ and need to identify the value of $$a$$ and the vertex of the graph. 2. **Formula and explanation:** The ge

1. The problem is to solve a system of 2 simultaneous inequalities. 2. A system of inequalities involves finding the set of values that satisfy both inequalities at the same time.

1. **Problem Statement:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula and Rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we use the q

1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and asked to understand its graph and properties. 2. **Formula and explanation:** The function involves the a

1. **State the problem:** We want to solve simultaneous inequalities using MATLAB. 2. **Understanding simultaneous inequalities:** These are multiple inequalities that must be true

1. **State the problem:** We have a piecewise function $$k(x) = \begin{cases} \sqrt[3]{x+1} & \text{if } x < 8 \\ -8x + 1 & \text{if } 8 \leq x \leq 16 \\ x + 3 & \text{if } x > 16

1. **State the problem:** We are given a piecewise function: $$m(x) = \begin{cases} 20x + 25 & \text{if } x < 0 \\ 11 - 7x & \text{if } x \geq 0 \end{cases}$$

1. The problem asks to find the exact value of $k(9)$ given the piecewise function: $$k(x) = \begin{cases} x^2 & \text{if } x < 5 \\ x + 2 & \text{if } x = 5 \\ 2 - x & \text{if }

1. The problem is to find the correct graph for the linear equation $3x + 2y = 4$. 2. To graph a linear equation, we find the intercepts where the line crosses the axes.

1. The problem asks to solve a system, but no explicit system of equations is provided in the message. 2. Since no equations or expressions are given, we cannot perform algebraic m

1. Énoncé du problème : Montrer que la fonction $f$ définie par $$f(x) = \frac{1}{x^2 + 2x + 2}$$ est bijective de l'intervalle $[-1, +\infty[$ vers son image, puis déterminer sa f

1. Gegeben ist die Funktion $f(x) = \sqrt{x}$ und ihr Graph $K_f$. 2. Der Graph $K_h$ entsteht durch eine Spiegelung von $K_f$ an der $x$-Achse. Das bedeutet, dass alle $y$-Werte v