Questions: The figure to the right shows the average price of silver for recent years. Let S(t) represent the average price (in dollars per ounce) of silver for year t. Answer parts (a) through ( g ) below. (a) Is S(t) a linear function? A. No, because it increases and decreases B. Yes, because it increases C. Yes, because it consists of a collection of straight line segments D. No because S(t) is not a multiple of t (b) What is the independent variable? A. ounces, x B. year, t C. average price of silver, S(t) D. dollars, S (c) What is the dependent variable? A. average price of silver, S(t) B. year, t C. dollars, x D. ounces, S (d) What is the domain of the function? The domain is . (Type your answer in interval notation.)

The figure to the right shows the average price of silver for recent years. Let S(t) represent the average price (in dollars per ounce) of silver for year t. Answer parts (a) through ( g ) below. (a) Is S(t) a linear function? A. No, because it increases and decreases B. Yes, because it increases C. Yes, because it consists of a collection of straight line segments D. No because S(t) is not a multiple of t (b) What is the independent variable? A. ounces, x B. year, t C. average price of silver, S(t) D. dollars, S (c) What is the dependent variable? A. average price of silver, S(t) B. year, t C. dollars, x D. ounces, S (d) What is the domain of the function? The domain is . (Type your answer in interval notation.)
Transcript text: The figure to the right shows the average price of silver for recent years. Let $\mathrm{S}(\mathrm{t})$ represent the average price (in dollars per ounce) of silver for year t. Answer parts (a) through ( g ) below. (a) Is $\mathrm{S}(\mathrm{t})$ a linear function? A. No, because it increases and decreases B. Yes, because it increases C. Yes, because it consists of a collection of straight line segments D. No because $\mathrm{S}(\mathrm{t})$ is not a multiple of $t$ (b) What is the independent variable? A. ounces, $x$ B. year, $t$ C. average price of silver, $\mathrm{S}(\mathrm{t})$ D. dollars, $S$ (c) What is the dependent variable? A. averagelprice of silver, $\mathrm{S}(\mathrm{t})$ B. year, $t$ C. dollars, $x$ D. ounces, $S$ (d) What is the domain of the function? The domain is $\square$ . (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Determine if S(t) is a linear function

A linear function increases or decreases at a constant rate. The graph of S(t) increases, decreases, and increases again, meaning its rate of change is not constant. Thus, it's not a linear function.

Step 2: Identify the independent variable

The independent variable is the input of the function, which in this case is _t_, representing the year.

Step 3: Identify the dependent variable

The dependent variable is the output of the function, determined by the input value. Here, the dependent variable is S(t), the average price of silver.

Final Answer:

(a) No, because it increases and decreases. (b) year, t (c) average price of silver, S(t)

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