Question
Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?
- A linear function whose rate of change is not zero
- A quadratic function with real zeros
- A quadratic function with no real zeros
- A cubic polynomial with at least one real zero
The correct answer is: A quadratic function with no real zeros
Solution:- Option(C) A quadratic function with no real zeros.
Lets consider option A, it says that A linear function whose rate of change is not zero.
- Rate of change = Slope of the line
We know that, equation of line is y = mx + c ,
In the question we have given that function has no x-intercept. That means it should not intersect the x-axis. i.e.it should be parallel to the x-axis.
Now, x-axis is the line such that its slope, m= 0 and y-intercept, c=0.
But as in the given option rate of change is not zero that means slope m≠0. So the line will not be parallel to x-axis. Hence, it will have x-intercept at some point.
So, Option A is not correct.
Lets consider option B, it says that a quadratic function with real zero,
We know that, A zero or root of a function is the value of x at which the function is zero.
So, when we draw graph then, (x, y) = (x, f(x))
So, at real zero value of x is (x1 , 0) where x1 is real zero.
If the function has real zeros it will intersect x-axis at some point because function will be equal to zero at the value of the real zero.
So, Option B is not correct.
Lets consider option C, it says that a quadratic function with no real zeroes.
So, function with no real zeroes, will not be equal to 0 at any real value of x. Hence there will be no x-intercept.
So, Option C is Correct .
Reason for option D will be same as of Option B.
Related Questions to study
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The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.
In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
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So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
To calculate average miles, divide the total distance traveled by the time spent traveling. This will provides us with your average speed.
So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
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The circle above with center O has a circumference of 36. What is the length of minor arc 
?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
The circle above with center O has a circumference of 36. What is the length of minor arc ?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
