🧮 algebra

1. The problem asks to find the value of $y$ for $y = f(1)$ using the graph of the function $f$.\n2. From the description, the graph has a local maximum near $(0,5)$, a local minim

1. The problem asks to find the value of $x$ when $f(x) = 3$ using the graph of the function $f$. 2. The function value $f(x)$ represents the $y$-coordinate on the graph for a give

1. **State the problem:** We need to find the amount $A$ using the formula for simple interest: $$A = P(1 + rt)$$ where $P$ is the principal, $r$ is the interest rate per year, and

1. **State the problem:** We are asked to perform the matrix multiplication of two 2x2 matrices: $$\begin{bmatrix} 5 & 6 \\ -9 & -1 \end{bmatrix} \times \begin{bmatrix} -1 & -8 \\

1. **State the problem:** We need to find the principal amount $P$ given the simple interest $I=18$, the rate $r=6\%$, and the time $t=3$ months. 2. **Formula:** The simple interes

1. The problem asks to describe the transformations to obtain the graph of $g(x) = 6^{x - 7}$ from the graph of $f(x) = 6^x$. 2. Recall the general rule for horizontal shifts in ex

1. The problem asks to graph the function $$y = 2^x$$ over the interval $$[-4,4]$$. 2. The function $$y = 2^x$$ is an exponential function with base 2, which means it grows rapidly

1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{x^2 + 5}{(x^2 - 25)(x^2 - 64)}.$$\n\n2. **Recall the rule for vertical asymptotes:** Vertical

1. **State the problem:** Find the horizontal asymptote(s) of the function $$f(x) = \frac{5x^2 + 4x + 4}{4x^2 + 5x - 3}$$. 2. **Recall the rule for horizontal asymptotes:**

1. The problem is to graph the piecewise function: $$f(x) = \begin{cases} 1 - 2x & \text{if } x < 2 \\ x - 3 & \text{if } x \geq 2 \end{cases}$$

1. **State the problem:** We need to graph the piecewise function $$f(x) = \begin{cases} 1 - 2x & \text{if } x < 2 \\ x - 3 & \text{if } x \geq 2 \end{cases}$$

1. The problem asks how the graph of $g(x) = -|x - 5|$ relates to the graph of $f(x) = |x|$ and to sketch the graph of $g(x)$. 2. Recall the base function $f(x) = |x|$ is a V-shape

1. The problem asks us to find the domain of the function $$g(x) = \sqrt{3 - x}$$. 2. The domain of a function involving a square root requires the expression inside the root to be

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x - 9}{x + 3}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers

1. **Stating the problem:** Undersök hur många procent $P = x \cdot y$ ökar om $x$ ökar med 10 % och $y$ ökar med 20 %.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x - 9}{x + 5}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers

1. The problem asks to find the value of $y$ for $y = f(1)$ using the graph of the function $f$. 2. From the description, the graph has a local maximum near $y=5$ at $x=0$, a local

1. Problemet handlar om att hitta elpriset per kWh år 2013, givet att priset år 2014 var 27 öre och att detta pris var 40 % lägre än året innan. 2. Formeln för att beräkna ursprung

1. The problem asks to evaluate the permutation expression $6P5$. 2. The formula for permutations is:

1. The problem asks to evaluate the combination $15C2$, which represents the number of ways to choose 2 items from 15 without regard to order. 2. The formula for combinations is:

1. **State the problem:** Find the y-intercept and x-intercepts of the function $$g(x) = -(x+5)^2 + 8$$ and describe the graph shape. 2. **Y-intercept:** The y-intercept occurs whe