Which of the following statements about…

Maths Questions

Which of the following statements about the graph of the function y = 2^x are true? Check all boxes that apply. 1. The domain is all real numbers x because the exponent can be any real number. 2. When the x-values increase by 1 unit, the y-value multiplies by 2. 3. The y-intercept is (0, 1). 4. The graph never goes below the x-axis because powers of 2 are never negative. 5. The range is all real numbers.

Answer

The correct options are 1, 2, 3, and 4. Here’s the step-by-step breakdown: The function in question is [tex]f(x)=2^x[/tex] This function is defined for every real number x, indicating that the domain encompasses all real numbers. As x serves as the exponent for 2, an increase in x by 1 unit results in the y-value being doubled. To determine the y-intercept, we set x=0: [tex]f(0)=2^0=1[/tex] Thus, the y-intercept is (0, 1). Since powers of 2 are inherently positive, the value of f(x) remains greater than 0, ensuring that the graph will not dip below the x-axis. Because of this, the range of the function consists of all positive real numbers. So, the correct options remain 1, 2, 3, and 4.

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