What is the domain and range fro the expentiral function f(x)=-2x4^x-1+3?
Domain:all real numbers
Range:all real numbers less than 3
Domain:all real numbers
Range:all real numbers greater than 3
Domain: all real numbers greater than-2
Range: all real numbers less than 3
Domain: all real numbers
Range: all real numbers
If the parent function is f(x) = (0.5)^x, which transformations are required for the graph of f(x) = (0.5)^x-3 - 2?
Translate 3 units right and 2 units up
Translate 3 units right and 2 units down
Translate 3 units left and 2 units up
Translate 3 units left and 2 units down
How do I figure something like this out... I'm lost once again
Assuming you meant
f(x)=-2x*4^(x-1)+3
the domain of all polynomials (-2x) is (-∞,∞)
the domain of all exponentials is (-∞,∞)
so, the domain of f(x) is likewise (-∞,∞)
now work with the ranges in like wise.
x -> (x-h) translates right by h
y -> (y-k) translates up by k
y = 0.5^(x-3) - 2 is also
y-(-2) = 0.5^(x-3)
so what do you think?
Thanks Mr.Steve!
To find the domain and range of a function, you need to consider the restrictions and values that the function can take.
For the given exponential function f(x) = -2x*4^(x-1) + 3, we can analyze the restrictions for the domain and the possible values for the range:
1. Domain: The domain of an exponential function is typically all real numbers, unless there are any specific restrictions such as logarithmic functions where the base cannot be zero or a negative number. In this case, there are no such restrictions, so the domain is all real numbers.
2. Range: The range represents the set of all possible output values of the function. For an exponential function, if the base is positive and not equal to 1, then the range is either all positive numbers (for an upward-facing graph) or all negative numbers (for a downward-facing graph). In this case, the base is 4, which is positive and not equal to 1.
Given that the constant term 3 is added to the function, it shifts the entire graph vertically. Since 3 is positive, the entire graph is shifted upward by 3 units. Therefore, the range of the function is all real numbers greater than 3.
As for the second question, to determine the transformations required for the graph of f(x) = (0.5)^x-3 - 2 compared to the parent function f(x) = (0.5)^x, you need to understand the effect of the added constant and the exponent's change.
1. Translate 3 units right: The transformation f(x-3) causes the graph to shift horizontally by 3 units to the right.
2. Translate 2 units down: The transformation f(x) - 2 shifts the graph vertically downward by 2 units.
Therefore, the correct answer is "Translate 3 units right and 2 units down."
If you are lost in similar problems, try breaking down the transformations into separate steps and visualize their effects on the graph. Remember to understand the general principles behind each transformation (vertical shifts, horizontal shifts, stretching, compressing). Practice with simpler examples to gain more confidence in solving these types of problems.