Which two are true comparisons for the following functions f(x) and g(x)? 




f(x)















A

the slope of 𝑓<f \ltf< the slope of 𝑔gg 

B

𝑓(1)=𝑔(1)f(1)=g(1)f(1)=g(1)

C

𝑓(2)>𝑔(2)f(2) \gt g(2)f(2)>g(2)

D

the 𝑦yy-intercept of 𝑓=f=f= the 𝑦yy-intercept of 𝑔gg 



REVIEW/END TEST

PAUSE

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It seems like you are comparing two functions \( f(x) \) and \( g(x) \) based on certain properties such as their slopes, values at specific points, and \( y \)-intercepts. Without the explicit definitions or graphs of the functions \( f(x) \) and \( g(x) \), it’s challenging to determine the correct comparisons directly. However, I can provide a guide on how to analyze each option:

### A. **The slope of \( f(x) \) is less than the slope of \( g(x) \)**
- This comparison is about the rate of change of each function. If both \( f(x) \) and \( g(x) \) are linear functions (in the form \( y = mx + b \)), the slope is the coefficient \( m \). Check if the slope of \( f(x) \) is less than the slope of \( g(x) \).

### B. **\( f(1) = g(1) \)**
- This means that at \( x = 1 \), both functions give the same output. To check this, you would evaluate both functions at \( x = 1 \) and compare the results.

### C. **\( f(2) > g(2) \)**
- Here, you would evaluate both functions at \( x = 2 \) and check if \( f(2) \) is greater than \( g(2) \).

### D. **The \( y \)-intercept of \( f(x) \) is equal to the \( y \)-intercept of \( g(x) \)**
- The \( y \)-intercept is the point where the function crosses the \( y \)-axis, which happens when \( x = 0 \). You would compare \( f(0) \) and \( g(0) \) to see if they are equal.

### To determine which two statements are true, you would need the specific expressions or graphs for \( f(x) \) and \( g(x) \). 

Do you have the functions or a graph for more context? Feel free to upload any images or details.

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Here are five related questions:
1. How do you determine the slope of a function from its equation?
2. What does it mean for two functions to have the same \( y \)-intercept?
3. How can you find the value of a function at a specific point, such as \( f(1) \)?
4. What does it mean for one function's value to be greater than another's at a given point?
5. What are the key differences between a linear and a non-linear function in terms of slopes?

**Tip**: Always check for critical points like \( x = 0 \), which gives the \( y \)-intercept, and points like \( x = 1 \) or \( x = 2 \) for comparisons.

Which two are true comparisons for the following functions f(x) and g(x)? 

f(x)

A. The slope of f(x) < the slope of g(x) 
B. f(1) = g(1) 
C. f(2) > g(2) 
D. The y-intercept of f(x) = the y-intercept of g(x)

Learn how to compare two functions by analyzing their slopes, y-intercepts, and values at specific points such as f(1) and g(1). This problem explores key algebraic concepts including the slope-intercept form and function evaluation, suitable for Grades 9-11.

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