Question

Which function(s) have a limited domain? Select all that apply.(2 points)
Responses

y=|x|
y is equal to absolute value of x

y=x−−√
y is equal to square root of x

y=x−−√3
y is equal to cube root of x

y=x2
y is equal to x squared

y=x
y is equal to x

y=logbx
y is equal to the log base b of x

y=bx
y is equal to b to the x th power
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Answer 1

To determine which functions have a limited domain, let's analyze each function:

1. **y = |x|**: The absolute value function is defined for all real numbers. **Domain: All real numbers.**

2. **y = √x**: The square root function is only defined for non-negative numbers (x ≥ 0). **Domain: x ≥ 0 (limited domain).**

3. **y = ∛x**: The cube root function is defined for all real numbers. **Domain: All real numbers.**

4. **y = x²**: The squaring function is defined for all real numbers. **Domain: All real numbers.**

5. **y = x**: The identity function is defined for all real numbers. **Domain: All real numbers.**

6. **y = log_b(x)**: The logarithm function is only defined for positive real numbers (x > 0). **Domain: x > 0 (limited domain).**

7. **y = b^x**: The exponential function is defined for all real numbers. **Domain: All real numbers.**

From this analysis, the functions with a limited domain are:

- **y = √x**
- **y = log_b(x)**

So, the responses that apply are:

- y = √x
- y = log_b(x)