Podcast
Questions and Answers
A line passes through the point (2, 2) and has a slope of $-\frac{3}{7}$. Which of the following is the equation of this line?
A line passes through the point (2, 2) and has a slope of $-\frac{3}{7}$. Which of the following is the equation of this line?
- $y = -\frac{3}{7}x - \frac{20}{7}$
- $y = \frac{3}{7}x - \frac{20}{7}$
- $y = -\frac{3}{7}x + \frac{20}{7}$ (correct)
- $y = \frac{3}{7}x + \frac{20}{7}$
What are the slope and y-intercept of the line given by the equation $2x + 5y = 19$?
What are the slope and y-intercept of the line given by the equation $2x + 5y = 19$?
- Slope: $\frac{2}{5}$, y-intercept: $-\frac{19}{5}$
- Slope: $\frac{5}{2}$, y-intercept: $\frac{19}{5}$
- Slope: $-\frac{2}{5}$, y-intercept: $\frac{19}{5}$ (correct)
- Slope: $-\frac{5}{2}$, y-intercept: $-\frac{19}{5}$
What is the range of the function $y = x^2 - 5$?
What is the range of the function $y = x^2 - 5$?
- $(-\infty, \infty)$
- $\left[-5, \infty\right)$ (correct)
- $\left(0, \infty\right)$
- $\left(-\infty, -5\right]$
Consider the piecewise-defined function: $f(x) = \begin{cases} -2, & x \leq 0 \ x + 1, & x > 0 \end{cases}$. Which of the following statements best describes the graph of this function?
Consider the piecewise-defined function: $f(x) = \begin{cases} -2, & x \leq 0 \ x + 1, & x > 0 \end{cases}$. Which of the following statements best describes the graph of this function?
If $f(x) = -6x + 4$ and $g(x) = 2x + 7$, what is $g(f(x))$?
If $f(x) = -6x + 4$ and $g(x) = 2x + 7$, what is $g(f(x))$?
Flashcards
Find the equation of a line passing through (2, 2) with slope -3/7
Find the equation of a line passing through (2, 2) with slope -3/7
The equation of a line passes through a given point (2, 2) and has a slope of -3/7. It is written in the slope-intercept form (y = mx + c): y = -3/7x + 20/7.
Finding the slope and y-intercept of 2x + 5y = 19
Finding the slope and y-intercept of 2x + 5y = 19
The slope-intercept form of the equation of a linear function is y = mx + c, where m represents the slope and c represents the y-intercept. In this case, the slope is -2/5 and the y-intercept is 19/5.
What is the domain and range of y = x² - 5?
What is the domain and range of y = x² - 5?
For a polynomial function, the domain is all real numbers (-∞, ∞) since you can plug in any real number for x. The range is all real numbers greater than or equal to -5 ([-5, ∞]) because the graph is a parabola opening upwards with a vertex at -5.
Graphing a piecewise function
Graphing a piecewise function
Signup and view all the flashcards
Finding the composite function g(f(x)) for f(x) = -6x + 4 and g(x) = 2x + 7
Finding the composite function g(f(x)) for f(x) = -6x + 4 and g(x) = 2x + 7
Signup and view all the flashcards
Study Notes
Equation of a Line
- Given a point (2, 2) and slope -3, the equation is y = -3x + 8
- The slope of the line 2x + 5y = 19 is -2/5
- The y-intercept is 19/5
Domain and Range
- For the function y = x² - 5, the domain is all real numbers
- The range is y ≥ -5
Piecewise Function
- The function f(x) is defined as x + 1 if x ≤ 0 and x if x > 0.
- The graph of this function has a point at (0, 1). When x=0, and when x=2 the function goes through point (2, 2).
Function Composition
- Given f(x) = -6x + 4 and g(x) = 2x + 7, g(f(x)) = -12x + 15
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers key concepts in algebra, including the equations of lines, domain and range, piecewise functions, and function composition. Test your understanding of these fundamental topics with practical examples and problem-solving scenarios.
