the range is all real numbers
apex what is the range of the absolute... answer is nonnegative real num...
No, the y-intercept is not the same as the absolute value parent function. The absolute value parent function, represented as ( f(x) = |x| ), has a vertex at the origin (0, 0), which serves as its y-intercept. While the absolute value function does have a specific y-intercept, the term "y-intercept" generally refers to the point where any function crosses the y-axis, which can vary depending on the function in question.
The domain of the absolute value parent function, ( f(x) = |x| ), is all real numbers, expressed as ( (-\infty, \infty) ). The range is all non-negative real numbers, represented as ( [0, \infty) ), since the absolute value cannot be negative.
To shift the absolute value parent function ( F(x) = |x| ) right by 9 units, you replace ( x ) with ( x - 9 ). Therefore, the equation of the new function becomes ( F(x) = |x - 9| ). This transformation moves the vertex of the absolute value function from the origin to the point (9, 0).
To horizontally shift the absolute value parent function ( F(x) = |x| ) three units to the left, you replace ( x ) with ( x + 3 ). This results in the new function ( F(x) = |x + 3| ). Thus, the equation of the shifted function is ( F(x) = |x + 3| ).
apex what is the range of the absolute... answer is nonnegative real num...
No, the y-intercept is not the same as the absolute value parent function. The absolute value parent function, represented as ( f(x) = |x| ), has a vertex at the origin (0, 0), which serves as its y-intercept. While the absolute value function does have a specific y-intercept, the term "y-intercept" generally refers to the point where any function crosses the y-axis, which can vary depending on the function in question.
The domain of the absolute value parent function, ( f(x) = |x| ), is all real numbers, expressed as ( (-\infty, \infty) ). The range is all non-negative real numbers, represented as ( [0, \infty) ), since the absolute value cannot be negative.
It’s vertex is not at the origin
apex what is the range of the absolute... answer is nonnegative real num...
Its vertex is not at the origin
The absolute value function returns the absolute value of a number.
To shift the absolute value parent function ( F(x) = |x| ) right by 9 units, you replace ( x ) with ( x - 9 ). Therefore, the equation of the new function becomes ( F(x) = |x - 9| ). This transformation moves the vertex of the absolute value function from the origin to the point (9, 0).
An absolute-value function
To horizontally shift the absolute value parent function ( F(x) = |x| ) three units to the left, you replace ( x ) with ( x + 3 ). This results in the new function ( F(x) = |x + 3| ). Thus, the equation of the shifted function is ( F(x) = |x + 3| ).
No it is not
No, There exists a counter example in the page 244 of the book Grimmett & Stirzaker, One thousand exercises in probability. The example is a Bernoulli random variable with parameter 1/3.