Question
Describe how the graph of – 12 is like the graph of mc019-2.jpg and how it is different.
The graphs are the same shape. The y-intercept of is 0 and the x-intercept of mc019-6.jpg – 12 is –12.
The graphs are the same shape. The y-intercept of is 0 and the y-intercept of mc019-8.jpg – 12 is –12.
The graph of – 12 is the same as mc019-10.jpg.
The graphs have the same y-intercept. The graph of – 12 is steeper than mc019-4.jpg.
The graphs are the same shape. The y-intercept of is 0 and the x-intercept of mc019-6.jpg – 12 is –12.
The graphs are the same shape. The y-intercept of is 0 and the y-intercept of mc019-8.jpg – 12 is –12.
The graph of – 12 is the same as mc019-10.jpg.
The graphs have the same y-intercept. The graph of – 12 is steeper than mc019-4.jpg.
Answers
GPT-4o mini
To compare the graph of the function \( f(x) = x - 12 \) to the graph of a given function (let's denote it as \( g(x) \)), we can analyze several aspects:
1. **Shape of the Graph**: Both graphs have the same shape if they are linear functions. They will both be straight lines.
2. **Y-Intercept**: The y-intercept of the function \( f(x) = x - 12 \) is -12, since when \( x = 0 \), \( f(0) = 0 - 12 = -12 \). For the graph of \( g(x) \), we would also determine its y-intercept.
3. **X-Intercept**: The x-intercept of \( f(x) = x - 12 \) can be found by setting \( f(x) = 0 \). This gives \( x - 12 = 0 \), or \( x = 12 \). The x-intercept of the function \( g(x) \) would depend on its equation.
4. **Steepness**: The steepness (or slope) of the line depends on the coefficients of \( x \). If \( f(x) = x - 12 \) has a slope of 1, it can be compared to the slope of \( g(x) \).
Given all the information provided in your options, we can evaluate:
- The first option references the y-intercept of \( g(x) \) being 0, which is not the case for \( f(x) \).
- The second option compares the y-intercepts but again inaccurately states \( g(x) \) has a y-intercept of 0.
- The third option claims \( f(x) \) and \( g(x) \) are the same, which depends on the definition of \( g(x) \).
- The fourth option states that \( f(x) \) is steeper than \( g(x) \) and mentions a common y-intercept.
Without knowing the specifics of \( g(x) \), it is challenging to definitively choose one of the statements. However, a typical correct statement would note that both functions are linear, mentioning their y-intercepts and/or slopes, thus allowing for correct comparisons to be made when given appropriate details about \( g(x) \).
1. **Shape of the Graph**: Both graphs have the same shape if they are linear functions. They will both be straight lines.
2. **Y-Intercept**: The y-intercept of the function \( f(x) = x - 12 \) is -12, since when \( x = 0 \), \( f(0) = 0 - 12 = -12 \). For the graph of \( g(x) \), we would also determine its y-intercept.
3. **X-Intercept**: The x-intercept of \( f(x) = x - 12 \) can be found by setting \( f(x) = 0 \). This gives \( x - 12 = 0 \), or \( x = 12 \). The x-intercept of the function \( g(x) \) would depend on its equation.
4. **Steepness**: The steepness (or slope) of the line depends on the coefficients of \( x \). If \( f(x) = x - 12 \) has a slope of 1, it can be compared to the slope of \( g(x) \).
Given all the information provided in your options, we can evaluate:
- The first option references the y-intercept of \( g(x) \) being 0, which is not the case for \( f(x) \).
- The second option compares the y-intercepts but again inaccurately states \( g(x) \) has a y-intercept of 0.
- The third option claims \( f(x) \) and \( g(x) \) are the same, which depends on the definition of \( g(x) \).
- The fourth option states that \( f(x) \) is steeper than \( g(x) \) and mentions a common y-intercept.
Without knowing the specifics of \( g(x) \), it is challenging to definitively choose one of the statements. However, a typical correct statement would note that both functions are linear, mentioning their y-intercepts and/or slopes, thus allowing for correct comparisons to be made when given appropriate details about \( g(x) \).