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Is it true a polynomials real roots are the values at which the graph of a polynomial meets the x axis?
Yes, that is true. The real roots of a polynomial are the values of ( x ) for which the polynomial evaluates to zero, which corresponds to the points where the graph intersects the x-axis. In other words, if ( f(x) = 0 ) for some real number ( x ), then the graph of the polynomial ( f(x) ) will cross the x-axis at that point.
What else can I help you with?
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
How you write a polynomal function with least degree?
To write a polynomial function of least degree that fits given points, identify the x-values and corresponding y-values you want the function to pass through. The least degree polynomial is determined by the number of unique points: for ( n ) points, the least degree polynomial is ( n-1 ). Use methods such as polynomial interpolation (e.g., Lagrange interpolation or Newton's divided differences) to construct the polynomial that meets these conditions, ensuring it passes through all specified points.
Is -4x a polynomial?
Yes, -4x is a polynomial. A polynomial is an expression that consists of variables raised to non-negative integer powers, multiplied by coefficients. In this case, -4 is the coefficient and x is the variable raised to the first power, which meets the criteria for a polynomial. Thus, -4x is a linear polynomial.
Is a positive graph a function?
A positive graph refers to a graph where all the values of the dependent variable (typically y) are greater than zero. Whether a positive graph represents a function depends on whether each input (x-value) corresponds to exactly one output (y-value). If it meets this criterion, regardless of being above the x-axis, it is indeed a function. Conversely, if any x-value maps to multiple y-values, it is not a function, even if the outputs are positive.
When do you say that a graph is a function?
In simple terms, if a vertical line meets a graph in more than one place it is not a function.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
Is it true that a polynomial's real roots are the values at which the graph of a polyomial meets the x-axis?
Yes.
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
How you write a polynomal function with least degree?
To write a polynomial function of least degree that fits given points, identify the x-values and corresponding y-values you want the function to pass through. The least degree polynomial is determined by the number of unique points: for ( n ) points, the least degree polynomial is ( n-1 ). Use methods such as polynomial interpolation (e.g., Lagrange interpolation or Newton's divided differences) to construct the polynomial that meets these conditions, ensuring it passes through all specified points.
Is -4x a polynomial?
Yes, -4x is a polynomial. A polynomial is an expression that consists of variables raised to non-negative integer powers, multiplied by coefficients. In this case, -4 is the coefficient and x is the variable raised to the first power, which meets the criteria for a polynomial. Thus, -4x is a linear polynomial.
Why does f represent the graph of a function?
Because each vertical lines meets its graph in a unique point.
Is a positive graph a function?
A positive graph refers to a graph where all the values of the dependent variable (typically y) are greater than zero. Whether a positive graph represents a function depends on whether each input (x-value) corresponds to exactly one output (y-value). If it meets this criterion, regardless of being above the x-axis, it is indeed a function. Conversely, if any x-value maps to multiple y-values, it is not a function, even if the outputs are positive.
When do you say that a graph is a function?
In simple terms, if a vertical line meets a graph in more than one place it is not a function.
What does y intercept mean?
anywhere a line, on a graph, meets with the y axis
When does a graph represents a function?
take a vertical line, if another line intersects that vertical line at 2 points, then it is a function.In other words,a graph represents a function if each vertical line meets its graph in a unique point.
How would you gaph the equation y equals 2x minuis3?
You know that y = 2x - 3, so to draw the graph: (a) You work out where this equation meets the horizontal axis of the graph and put a mark there. (b) You also work out where it meets the vertical axis of the graph and put a mark there. You then draw a straight line through the two points which carries on on either side. For (a) the equation meets the horizontal axis when y = 0. You know that y = 2x - 3, so put y = 0 into this equation. 0 = 2x - 3 -> 3 = 2x -> x = 1.5 So the line meets the horizontal axis when x = 1.5 For (b) the equation meets the vertical axis when x = 0 So again put that into y = 2x - 3 So y = 2*0 - 3 -> y = -3 So the line meets the vertical axis when y = -3. Draw a line through these two points (1.5,0) and (0,-3) and there you have your graph.
Is x7 a function?
Yes, ( x^7 ) is a function. Specifically, it is a polynomial function where the input ( x ) is raised to the seventh power. As a polynomial, it is defined for all real numbers and has a smooth curve without any breaks or jumps. Thus, it meets the criteria of a function, mapping each input ( x ) to a unique output ( x^7 ).
