#1
Which of the following is a characteristic of linear functions?
Their graphs are always straight lines.
ExplanationLinear functions exhibit straight-line graphs.
#2
What is the general form of a linear function?
f(x) = ax + b
ExplanationThe general form of a linear function is expressed as f(x) = ax + b.
#3
What is the slope-intercept form of the equation of a line?
y = mx + b
ExplanationThe slope-intercept form is given by y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
#4
What is the y-intercept of the linear function f(x) = 3x + 7?
7
ExplanationThe y-intercept is the constant term 'b' in the linear function, which is 7 in this case.
#5
If f(x) = 2x + 3 and g(x) = 3x - 2, what is the value of (f + g)(4)?
18
ExplanationAdding the two functions and substituting x = 4 gives the result of 18.
#6
Which of the following functions is linear?
f(x) = 2x + 3
ExplanationThe given function is linear because it has a first-degree term (2x).
#7
What is the slope of the line represented by the equation y = 3x - 2?
3
ExplanationThe coefficient of the x term in the equation represents the slope, which is 3.
#8
Which of the following is true about the composition of linear functions?
The composition of linear functions is always linear.
ExplanationComposing linear functions results in another linear function.
#9
What is the point-slope form of the equation of a line?
y - y1 = m(x - x1)
ExplanationThe point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and 'm' is the slope.
#10
If a linear function passes through the point (2, 5) and (6, 13), what is its slope?
3
ExplanationThe slope is determined by the change in y divided by the change in x, giving a slope of 3.
#11
Which of the following functions is not linear?
f(x) = sqrt(x)
ExplanationThe square root function is nonlinear, making the given function not linear.
#12
For a linear function f(x) = ax + b, what does 'a' represent?
Slope
Explanation'a' in the linear function represents the slope of the line.
#13
Which of the following is a property of linear functions?
They have a constant rate of change.
ExplanationLinear functions maintain a constant rate of change.
#14
What is the standard form of a linear equation in two variables?
ax + by = c
ExplanationThe standard form of a linear equation is represented as ax + by = c.
#15
If a linear function has a slope of 0, what can be said about the function?
It is a constant function.
ExplanationA slope of 0 indicates a constant function with no change.