| Topic | Problem | Solution |
|---|---|---|
| None | Determine which of the rational functions given b… | The x-intercept of a function is the value of x for which the function equals zero. For a rational … |
| None | Explain how the graph of the function $f(x)=\frac… | The function \(f(x)=\frac{1}{(x-2)^{2}}\) can be obtained from the function \(y=\frac{1}{x^{2}}\) b… |
| None | Find a possible equation for the function with a … | The function is a rational function because it has vertical and horizontal asymptotes. The x-interc… |
| None | Which of the following functions have a graph tha… | A vertical asymptote occurs when the denominator of a function is equal to zero. Therefore, we need… |
| None | $\sqrt{3 w+14}=\sqrt{7 w-14}$ | Given the equation \(\sqrt{3 w+14}=\sqrt{7 w-14}\) |
| None | What is the domain of $f(x)=\frac{1}{x}$ ? What i… | The domain of a function is the set of all possible input values (often the 'x' variable), which pr… |
| None | 3. The measure of two vertical angles are given b… | The problem is asking for the value of x and the measure of each angle. Vertical angles are angles … |
| None | 2. The measure of two verticle angles are $58^{\c… | Given that the measure of two vertical angles are $58^{\circ}$ and $(3x+4)^{\circ}$, we know that t… |
| None | 1. Find the value of $x$. \[ 5 x+11^{\circ}=4(x+6… | This is a simple algebraic equation. We need to solve for x. We can start by expanding the right si… |
| None | The graph of $f(x)=-x^{4}+x^{3}+8 x^{2}-12 x$ is … | The question is asking us to factor the function \(f(x)=-x^{4}+x^{3}+8 x^{2}-12 x\). The roots of t… |
| None | Suppose you have a 144-kg wooden crate resting on… | Given that the mass of the crate (m) is 144 kg, the acceleration due to gravity (g) is 9.8 m/s², th… |
| None | Find a polynomial of degree 3 with real coefficie… | We start by writing the polynomial of degree 3 with zeros at -3, -1, and 4 in the form \(f(x) = a(x… |
| None | The function $-x^{5}+36 x^{3}-22 x^{2}-147 x-90$ … | First, we need to find the roots of the polynomial from the graph. The roots are the x-values where… |
| None | Consider $f f(x)=3 x^{4}+6 x^{3}$ a. What is the … | The end behavior of a function refers to the behavior of the function as x approaches positive infi… |
| None | Rewrite the given equation in standard form. \[ x… | Rewrite the given equation in standard form. The equation is \(x=\frac{1}{8} y^{2}\). |
| None | A box contains 6 red balls, 4 green balls, and 2 … | The box contains 6 red balls, 4 green balls, and 2 blue balls. We are to pull 2 balls from the box … |
| None | John owns a hotdog stand. His profit is represent… | John owns a hotdog stand. His profit is represented by the equation \(P(x)=-x^{2}+12 x+41\), with \… |
| None | Graph the line. y-1=3(x-4) | This is a linear equation in point-slope form, \(y - y1 = m(x - x1)\), where m is the slope of the … |
| None | John owns a hotdog stand. He has found that his p… | John owns a hotdog stand. He has found that his profit is represented by the equation \(P(x)=-x^{2}… |
| None | Bob owns a watch repair shop. He has found that t… | The cost function is a quadratic function. The minimum value of a quadratic function \(f(x) = ax^2 … |
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