Which function has a range of {y|y ≤ 5}?

Step 1: Define the Problem

Identify which function has a range where all values of $y$ are less than or equal to 5.

Step 2: Break Down the Problem

Consider different types of functions and their typical ranges:

• Linear functions
• Quadratic functions
• Constant functions
• Exponential functions
• Logarithmic functions

Step 3: Apply Relevant Concepts

A function with a range of $\{y \mid y \leq 5\}$ implies that the maximum value of $y$ is 5, and all other values are less than or equal to 5. This is characteristic of functions that have a maximum point or are constant.

Step 4: Analysis, Verify and Summarize

• Constant Function: A function like $f(x) = 5$ has a range of $\{5\}$, which fits the condition $y \leq 5$.
• Quadratic Function: A downward-opening parabola, such as $f(x) = -x^2 + 5$, has a maximum point at $y = 5$ and decreases from there, fitting the range condition.
• Linear Function: A linear function like $f(x) = -x + 5$ can also have a range of $\{y \mid y \leq 5\}$ if it is decreasing.

Final Answer

A quadratic function such as $f(x) = -x^2 + 5$ or a constant function like $f(x) = 5$ has a range of $\{y \mid y \leq 5\}$.