Question
For the linear function f , the table above gives some values of x and their corresponding values f (x), where c is a constant. Which of the following equations defines f ?
- f (x) = x + c
- f (x) = x + 3c
- f (x) = cx + c
- f (x) = 3cx + 3c
The correct answer is: f (x) = cx + c
HINT :- Let the linear function be f(x) = ax + b substitute values and find a and b
Let the linear function be f(x) = ax + b
Step 1 : find b in terms of c
Let f(x) = ax + b at x =0 , f(x) = c
c = a(0) + b ⇒ ∴b = c
Step 2: find a in terms of c by substituting x = 1 and f(x) = 2c
lnf(x) = ax + b at x = 1 ,f(x) = 2c
2c = a(1) + b⇒ ∴a + b = 2c
Substitute b=c in the condition
a + b = a + c = 2c ⇒ a = c
As a = c and b = c then f(x) = cx + c.
Related Questions to study
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If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?
Energy per Gram of Typical Macronutrients
The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food
Refer to the following information.
If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?
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A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?
A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?
Club Participation in the 2014-2015 School Year
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Club Participation in the 2014-2015 School Year
Of all juniors and seniors who attended a particular high school during the 2014 -2015 school year, 149 participated in the clubs listed in the table above. Each of the 149 students participated in only one of the four school clubs listed. The table shows the distribution of the 149 students by class and club participation. Of the number of juniors and seniors in the drama club, the 25% who walked to school represents of the total number of juniors and seniors who walked to school. How many juniors and seniors walked to school?
The graph of the exponential function g in xy plane passes through the points (0,1), (1,4) and (2,16). Which of the following is NOT true?
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Which of the following is the value of y in the solution (x, y) to the system of equations above?
Which of the following is the value of y in the solution (x, y) to the system of equations above?
Club Participation in the 2014-2015 School Year
Of all juniors and seniors who attended a particular high school during the 2014 -2015 school year, 149 participated in the clubs listed in the table above. Each of the 149 students participated in only one of the four school clubs listed. The table shows the distribution of the 149 students by class and club participation.
The band was composed of freshmen, sophomores, juniors, and seniors. If 30% of the students in the band were juniors, how many students were in the band?
Club Participation in the 2014-2015 School Year
Of all juniors and seniors who attended a particular high school during the 2014 -2015 school year, 149 participated in the clubs listed in the table above. Each of the 149 students participated in only one of the four school clubs listed. The table shows the distribution of the 149 students by class and club participation.
The band was composed of freshmen, sophomores, juniors, and seniors. If 30% of the students in the band were juniors, how many students were in the band?
h(t) = -16t2 + 110t + 72 The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the
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Quadratic functions are expressed in the standard form. The terms are written in standard form in decreasing order, with the constant coming in last and the phrase with the highest exponent coming first.
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h(t) = -16t2 + 110t + 72 The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the
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Quadratic functions are expressed in the standard form. The terms are written in standard form in decreasing order, with the constant coming in last and the phrase with the highest exponent coming first.
The use of standard form is widespread. The format that is used when performing calculations on paper. A is 1, B is 5, and C is 6 in this illustration. There are additional forms, though.
The solutions or the roots of the quadratic equation are written as products to be multiplied in a different form known as factored form. The quadratic equation is a second-order polynomial equation in one variable with the formula x.
The equation x, a x 2 + bx + c = 0 with a ≠ 0 is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation guaranteed by the fundamental algebraic theorem. The answer could be simple or complicated.
In the figure above, 
, and 
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and 
, respectively. If AB = 9 , BC = 18.5 , and FE = 8.5, what is the length of 
to the nearest tenth?
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x + 5y = 5
2x - y = -4
Which of the following graphs in the xy-plane could be used to solve the system of equations above?
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A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm3, and the height of the can is 10 cm. If 110 cm3 of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?
A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm3, and the height of the can is 10 cm. If 110 cm3 of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?
Tanya earns $13.50 per hour at her part-time job. When she works z hours, she earns 13.50 z dollars. Which of the following expression gives the amount, in dollars, Tanya will earn if she works 3z hours?
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Percent of Residents who earned a bachelor’s degree or higher
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Percent of Residents who earned a bachelor’s degree or higher
A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?
In the xy - plane, which of the following changes to the graph of the equation y = x2 + 3 will result in the graph of the equation y = (x2 + 3) -6 ?
In the xy - plane, which of the following changes to the graph of the equation y = x2 + 3 will result in the graph of the equation y = (x2 + 3) -6 ?
The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?
A gram of Carbohydrates contain '4' calories, a gram of protein contains '4' calories, and a gram of fat contains '9' calories. Because one gram of fat contains '9' calories, divide the total number of calories by 9. 400, calories divided by 9 equals 44 grams. Then multiply 700 calories by 9 to obtain 78 grams.
To calculate total fat, look for the amount of fat found per serving of food in grams to determine its fat content. For example, if '1' teaspoon of butter weighs 4.7 grams and contains 3.8 grams of fat, you'll know that fat makes up about 80% of its weight.
The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?
A gram of Carbohydrates contain '4' calories, a gram of protein contains '4' calories, and a gram of fat contains '9' calories. Because one gram of fat contains '9' calories, divide the total number of calories by 9. 400, calories divided by 9 equals 44 grams. Then multiply 700 calories by 9 to obtain 78 grams.
To calculate total fat, look for the amount of fat found per serving of food in grams to determine its fat content. For example, if '1' teaspoon of butter weighs 4.7 grams and contains 3.8 grams of fat, you'll know that fat makes up about 80% of its weight.
