🧮 algebra

1. The problem asks how to translate the function $f(x) = 6^x$ to $g(x) = 6^{x - 5} - 7$. 2. Recall that for exponential functions, $f(x - h)$ shifts the graph horizontally by $h$

1. The problem asks to find the value of $h$ in the function $g(x) = 3^{x - h} + k$ given that $g(x)$ is a horizontal and vertical translation of $f(x) = 3^x$. 2. The function $g(x

1. The problem asks for the domain, range, and asymptote of the function $$h(x) = 2^{x+4}$$. 2. Recall that for an exponential function of the form $$f(x) = a^{x+c}$$ where $$a > 0

1. The problem asks to describe the translation of the function $f(x) = \left(\frac{1}{2}\right)^x$ to the function $g(x)$ based on the graph. 2. The original function is $f(x) = \

1. The problem involves understanding the transformations of the exponential function $f(x) = \left(\frac{1}{2}\right)^x$ and identifying the correct form of $g(x)$ after a transla

1. The problem is to solve the equation or expression implied by "do it". Since no specific problem is given, I will assume you want me to solve a simple algebraic example. 2. Let'

1. The problem is to understand and graph the function $g(x) = 2^x - 1 + 3$. 2. First, simplify the function by combining like terms:

1. The problem asks which translation steps change the function $f(x) = 3^x$ to $g(x) = 3^{x+1} + 4$. 2. Recall that for exponential functions, adding inside the exponent shifts th

1. The problem asks how to translate the function $f(x) = 3^x$ to $g(x) = 3^{x+1} + 4$. 2. Recall that adding inside the exponent, like $x+1$, shifts the graph horizontally. Specif

1. The problem asks for the domain of the function $f(x) = 3^{x-2}$. 2. The domain of an exponential function $a^x$ where $a > 0$ and $a \neq 1$ is all real numbers because you can

1. The problem asks for the domain of the function $f(x) = 3^{x-2}$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined.

1. **State the problem:** James has 60 pieces of fruit. \n\n1/12 of the fruit are mangos, and the rest are avocados. Mangos weigh 130g each, and avocados weigh 200g each. We need t

1. **State the problem:** We need to find how many glasses of milk can be filled from 1 7/8 jugs of milk if one glass holds 3/8 of a jug. 2. **Write the known quantities:**

1. The problem asks for the domain, range, and asymptote of the function $$h(x) = (0.5)^x - 9$$. 2. Recall that for an exponential function $$f(x) = a^x$$ where $$a > 0$$ and $$a \

1. The problem is to understand the graph of the function $$g(x) = (0.5)^{x + 3} - 4$$. 2. This is an exponential decay function because the base $$0.5$$ is between 0 and 1.

1. **State the problem:** Multiply the mixed numbers $1 \frac{2}{3}$ and $1 \frac{1}{6}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to im

1. **State the problem:** Solve the equation $$4^x - 13 \times 2^x + 40 = 0$$. 2. **Rewrite the equation using powers of 2:** Note that $$4^x = (2^2)^x = 2^{2x} = (2^x)^2$$.

1. El problema consiste en encontrar la ecuación general de una recta a partir de su forma punto-pendiente o cualquier otra forma. 2. La ecuación general de la recta se expresa com

1. El problema es encontrar la ecuación en forma general de una recta. 2. La forma general de la ecuación de una recta es $$Ax + By + C = 0$$ donde $A$, $B$ y $C$ son constantes re

1. **State the problem:** We need to make $x$ the subject of the formula given by $$2y^2 = \frac{5(x - 3)^5}{3y}.$$ 2. **Write down the formula and explain:** The goal is to isolat

1. **State the problem:** Calculate the value of $193^2 - 7^2$. 2. **Use the difference of squares formula:**